Friberg–LEO-GEO & GEO-GEO Stereo Imaging Diurnal Observations
Execisse Geo (9)
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1 . eKeGayrgVg;p©it O nigGgát;p©itBIrminEkgKña [AB] nig [CD]. KUsGgát;FñÚ [CE] Ekg [AB]. k > bgðajfa [DE] Rsb [AB] . x > R)ab;RbePTctuekaN AEDB . 2 . eKeGay [BH] nig [CK] CakMBs;énRtIekaN ABC . M kNþal [BC] . bgðajfa RtIekaN HKM sm)aT . 3 . eKeGayRtIekaN ABC carwkkñúgrgVg;p©it O nig M kNþalFñÚtUc AB . eKKUsGgát;FñÚ [MN] Rsb nig [BC] Edlkat; [AC]Rtg; S . RsaybMPøWfa SM=SC nig SA=SN . 4 . eKeGayRtIekaN CDE carwkkñúgrgVg;p©it O . M nig N kNþalerogén [EC] nig [ED] Edl [MN] kat;FñÚtUc ED Rtg; B nigFñÚtUc EC Rtg; A . RsaybMPøWfa ABCD CactuekaNBañysm)aT . 5 . eKeGayrgVg;BIrmanp©it O nig I ehIymankaM [OI] . rgVg;TaMgBIrkat;KñaRtg; A nig B . bnÞat;
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Transcript of Execisse Geo (9)
1
1 . eKeGayrgVg;pit O nigGgt;pitBIrminEkgKa [AB] nig [CD]. KUsGgt;F [CE] Ekg [AB].
k > bgajfa [DE] Rsb [AB] .
x > R)ab;RbePTctuekaN AEDB . 2 . eKeGay [BH] nig [CK] CakMBs;nRtIekaN ABC . M kNal [BC] .
bgajfa RtIekaN HKM sm)aT .
3 . eKeGayRtIekaN ABC carwkkgrgVg;pit O nig M kNalFtUc AB . eKKUsGgt;F [MN] Rsb nig [BC] Edlkat; [AC]Rtg; S .
RsaybMPWfa SM=SC nig SA=SN . 4 . eKeGayRtIekaN CDE carwkkgrgVg;pit O . M nig N kNalerogn [EC] nig [ED] Edl [MN] kat;FtUc ED Rtg; B nigFtUc EC Rtg; A . RsaybMPWfa ABCD CactuekaNBaysm)aT .
5 . eKeGayrgVg;BIrmanpit O nig I ehIymankaM [OI] . rgVg;TaMgBIrkat;KaRtg; A nig B . bnat; (OI) kat;rgVg;pit O Rtg; C nigrgVg;pit I Rtg; D . k > bgajfa CA=CB nig DA=DB .
x > rkRbePTctuekaN ACBD .
6 . eKeGayRtIekaN ABC RkgRtg; A Edl AB=a nig AC=3a . emdaTrn [AC] Rtg; I kat; [BC]Rtg; M nigknHbnat;BuHmMu A Rtg; P .
k > bgajfa RtIekaN AIP Ekgsm)aT . x > bMPWfa M kNal [BC] .
K > Rsayfa ABPM CaRbelLRkam .
7( . kgRtIekaN ABC KUsknHbnat;BuHmMukg nigeRkAnmMu B nig mMu C kat;KaRtg; S nig E . k > bMPWfa A ; E ; S rt;Rtg;Ka .
x > bgajfa ctuekaN BSCE carwkkgrgVg; .
8 . eKeGayctuekaN ABCD mYyman muM B nig muM D CamMuEkg . M enAelIGgt;RTUg [AC] .
tam M KUs [MN] Ekg [BC] Rtg; N rYcKYs [MP] Ekgnwg [AD] Rtg; P .
RsaybMPWfa
9 . eKeGayRtIekaNsm)aT ABC kMBUl A . D CacMenalEkgn B elI [AC] .
RsaybMPWfa
10(.eKeGayctuekaNBay ABCDman)attUc [AB] . knHbnat;BuHmMu A nig DRbsBVKaRtg; I. k > rkRbePTRtIekaN AID .
x > bMPWfa I enAelI)atmFm [MN] nctuekaNBay ABCD .
11 . kgRtIekaN ABC mYyKUskMBs; [BD] nig [CE] . kgRtIekaN ADE KUskMBs; [DF] nig [EG] .
k > eRbbeFob nig rYc nig .
x > RsaybMPWfa [FG] Rsbnwg [BC] . 12 . eKeGayctuekaNBay ABCD . bnayRCugeRTt [AD] nig [BC] kat;KaRtg; F . sal; nig . KNna .
13 . eKeGayRtIekaN ABCEkgRtg; A.tam E kNal [AC] KUs [ED] Ekgnwg [BC]Rtg; D . k > RbdUcRtIekaN ABC nig RtIekaN DEC .
x > bgajfa
14 . eKeGayRbelLRkam ABCD . E CacMnucmYyenAelIbnat; (BC) Edl C Carbs; [BE] . bnat; (AE) kat; (BD) Rtg; F nig [CD] Rtg; G . RsaybBaak;fa
15(( . eKeGayctuekaNBay ABCD .tam I CacMnucRbsBVnGgt;RTUg eKKUsbnat;Rsbnwg)at Edlkat;RCugeRTtTaMgBIrRtg; E nig F .
bgajfa I kNal [EF] .
16 . eKeGayRtIekaN ABC Ekg Rtg; A . eday . KNna BC . 17((. tamcMnuc E enAelI [AC] nRtIekaN ABC KUs [EF] Rsbnig [AB] Edlkat; [BC] Rtg; F tamcMnuc C KUsbnat;Rsbnig [AB] Edlkat;bnay (BE) Rtg; D .
RsaybMPWfa . 18 . KNna X tamrUbxageRkam D a . A eKeGay b . eKeGay A B 3 G 6 F 4 E 6 X C 4 D X E B F C19( . eKeGayRtIekaN MNP . eKKUskMBs; [NE] nig [PF] kat;KaRtg; H . knHbnat;BuHmMu M
kat; [NE] Rtg; A nig [PF] Rtg; B .
RsaybMPWfa RtIekaN HAB sm)aT .
20 . eKmanRtIekaN OAB tam M enAelI [OA] KUs [MN] Rsb nig [AB] tam N KUsbnt; [NP] Rsbnig [BM] . k > sresrRTwsIbTtaElskgRtIekaN ONP nig RtIekaN OBM .
x > sresrRTwsIbTtaElskgRtIekaN OMN nig RtIekaN OAB .
K > Tajfa .
21 . eKeGayRtIekaNsm)aT DEF kMBUl D . tamkMBUlnRtIekaNeKKUsbnat;mYYykat; [EF] Rtg; G nig kat;rgVg;carwkeRkARtIekaN DEF Rtg; H .
k > RbdUcRtIekaN DEG nig RtIekaN DEH .
x > bMPIfa . K > TajbBaak;fa .
22 . eKeGayrgVg;pit O Ggt;pit [AB] . bnat;mYyb:HrgVg;Rtg; M kat;bnay (AB) Rtg; P .
k > RbdUcRtIekaN AMP nig RtIekaN BMP .
x > Tajfa .
K > bMPWfa .
23 . eKeGayrgVg;BIr pit nig kat;KaRtg; A nig B . bnat;b:HeTAnigrgVg;TaMgBIrRtg; B kat; rgVg;TaMBIrerogKaRtg; C nig D .
k > RbdUcRtIekaN ABC nig RtIekaN ABD rYcTajvi)ak .
x > etIknHbnat; [AB) tagGVIcMeBaHmMu ?
K > RsaybMPWfa rYc . 24 . eKeGayRtIekaN ABC carwkkgrgVg;pit O . knHbnat;BuH kat; [BC] Rtg; M nig rgVg;Rtg; N . ( RblgqaM 1982 ) k > RsaybBaak;fa RtIekaN ABM dUc RtIekaN ANC .
x > KNna rYc bgajfa
K >Rsayfa . 25 . tamrUbxageRkam D RbdUcRtIekaN ABC nig RtIekaN ADC A 12 A 4 6 9 8 3 B C E 5 26 . tamrUbxageRkam x RbdUcRtIekaN ABC nig RtIekaN ADE . 7 D rYc KNna BC 1 B C 27 . eKeGayrgVg; O Ggt;pt [AB] mankaM R . bnat;mYykat;rgVg;Rtg; C nig D kat;bnay (AB) xag B Rtg; P .
k > RbdUcRtIekaN ACP nig RtIekaN DBP .
x > Tajfa .
K > Rsayfa .
28 . eKeGayRtIekaN ABC Ekg Rtg; A . (Rblg 1996 elIkTI 1 ) k > I kNal [BC] . R)ab;eQaHRtIekaN AIC .
x > O CacMnuckNaln [AB] . R)ab;eQaHctuekaN OICA .
K > KNna BC ebI AB = 6000 nig AC = 8000 .
X > rgVg;Ggt;pit [AB] nig [AC] kat;KaRtg; H .
a . bgajfa M enA elI [BC] .
b . Rsayfa
29 . eKeGayRtIekaNEkgsm)aT ABC eday AB = AC = a . ehIyDACkCaRtIekaN Ekg sm)aTkMBUl D . RtIekaNTaMgBIrenAsgxagRCugrYm [AC] .
k > kMnt;RbePTctuekaN ABCD .
x > KNna BC ; AD nig BD CaGnuKmn_n a .
K > Ggt;RTUg [AC]kat; [BD] Rtg; O. KNna OA ; OB ; OC ; OD CAGnuKmn_n a .
X > RbdUcRtIekaN AOD nig RtIekaN BOC rYcKNnapleFobdMNUc .
30 .((manGgt; [AB] mYy . C CacMnuckNal [AB] . ehIy D CacMnuckNal [BC] .
M CacMnucmYynbg; eday BM = BC . Rsayfa MA = 2 MD 31 . eKeGayRtIekaN ABC EkgRtg; A eday AB = a ; AC = a - 6 ; BC = a + 6 . KNnaRkLapRtIekaN ABC edayminCab; a .
32 . eKeGayRtIekaN ABC carwkkgrgVg;pit O kaM R . [AH] CakMBs;nRtIekaN ehIy [AD] CaGgtpit .
k > RsaybBaak;fa .
x > (AH) kat;rgVg;Rtg; E . Rsayfa . 33 . eKeGayrgVg;BIr ( O ) nig ( I ) kat;KaRtg; A nig B . tamcMnuc C enA elIbnay (AB) xag A eKKUsbnat; (CM) nig (CN) b:HeTAnigrgVg;TaMgBIrerogKaRtg; M nig N .
k > RbdUcRtIekaN CBM nig RtIekaN CAM rYcTajfa .
x > RbdUcRtIekaN CBN nig RtIekaN CAN .
K > Rsayfa CM = CN . X > bMPWfa .
34 . eKeGayrgVg;pit O Ggt;pit [AB] nigcMnuc C mYyenAelI [AB] . D CacMnucRbsBVmYyrvag rgVg;pit O nig rgVg;pit A man kaM [AC] . bnat; (CD) kat;rgVg;pit O Rtg; E . 1 > bgajfaRtIekaN ACD sm)aT .
2 > bgajfa .
3 > RbdUcRtIekaN CAD nig RtIekaN CEB .
4 > bgajfa RtIekaN ECB sm)aT
5 > bnat; (d) CaemdaTrn [BC] . bgajfa emdaTr (d) kat;tam E .
35 . eKeGayRtIekaNsmgS ABC . bnayRCug [BC] eGay)an BE=BC .
k > R)ab;eQaHRtIekaN AEC .
x > KNna AE ebI AC = 6cm .
K > KUsbnat;mYyEkgnig [CE] Rtg; C kat; (AE) Rtg; D. Rsayfa
36 . eKeGayRtIekaN ABC EkgRtg; A nigkMBs; [AH] . rgVg;Ggt;pit [AH] kat; [AB] nig [AC] erogKaRtg; D nig E . 1 > R)ab;RbePTctuekaN AEHD .
2 > RbdUcRtIekaN ABC nig RtIekaN ADE rYcTajfa .
3 > Rsayfa BDEC CactuekaNcarwkkgrgVg;EtmYy . 37 . eKeGayrgVg;BIrpit O nig I kat;KaRtg; A nig B . tam A KUsbnat;Rsbnig [OI] kat;rgVg; Rtg; C nig D . k > Rsyfa cMnuc B ; O ; C rt;Rtg;Ka .
x > Rsayfa cMnuc B ; I ; D rt;Rtg;Ka .
K > bgajfa CD = 2 IO .
38 . rgVg;BIr (O) nig ( I ) b:HKaxageRkARtg; A . bnat;mYyb:HrgVg; (O) Rtg; B nig rgVg; (I) Rtg; C bnat;b:HrYmRtg; A kat; (BC) Rtg; M . k > R)ab;eQaHctuekaN OBIC .
x > R)ab;eQaHRtIekaN ABC .
39 . eKeGayRtIekaN ABC KUs .
bgajfa . 40 . eKeGayRtIekaN ABC EkgRtg; A . KUs .
bgajfa .
41 . eKeGayRtIekaN ABC RBmTaMgkMBs; [AH] nig [BI] . Rsayfa AB . AC = BC . AH .
42 . ( eKeGayctuekaNEkg ABCD Edl (MA) Ekg (MB) M CacMnuckNaln [CD] .
KNnargVas;RCugnctuekaNEkg edaydwgfa brimaRtesI 24m . 43 . eKeGayrgVg;BIr nig ehIyb:HeRkArvagKa . rgVg;TaMgBIrenHb:HkgeTAnwgrgVg;TIbImYy eTotmanpit S . KNnakaMnrgVg;pit S edaydwgfabrimaRtn .
44 . eKeGayRtIekaN ABC Ekg Rtg; A man [AH] CakMBs; nig AB=5cm nig AC=12cm .
KNna BC ; AH ; BH ; CH . 45 . eKeGayrgVg;pit O kaM R Ggt;pit [AB] . (d) CaemdaTrn [OB] Rtg; I . M CacMnucmYyenAelIrgVg; . bnat; (MA) nig (MB) CYb (d) Rtg; N nig P . 1 > RbdUcRtIekaN ANI nigRtIekaN PBI rYcTajfa . 2 > bgajfa cMnuc A ; I ; I ; P nig M enAelIrgVg;EtmYyEdlRtUvbBaak;pit E .
3 > bgajfa (BN) Ekg nig (AB) .
46 . ctuekaNBaayEkgmYyman)atRbEvg 42cm nig 30 cm nigmankMBs;RbEvg 8cm . KNnargVas;RCugeRTt .
47 . bsSImYyedIm mankMBs; 10 m RtUvxl;vay)ak;Rtg; cMnuc M mYy . cugbsSI)ak;b:HdIRtg;cMnuc
mYyEdlmancMgay 3m BIKl;bsSI . KNnaRbEvgBIKl;bsSIeTAcMnuc)ak; M .
48 . eKeGayrgVg;pit OGgt;pit [CD]Edl CD=2R.[AB] CAGgt;FnrgVg;EdlRsbnig[CD]. k > R)ab;eQaHRtIekaN ACD . bgajfakgRtIekaNABC eKman .
x > bgajfa .
K > [AH] CakMBs;nRtIekaN ABC.RbdUc nig rYcTaj
49 . eKeGayRtIekaN ABC carwkkgrgVg; C(O;R) . bnat;KUstam B ehIyRsbnigbnat;b:HrgVg;
Rtg; A kat;bnat; (AC) Rtg; D . 1 > bgajfa RtIekaN ABC nig RtIekaN ADB dUcKa rYcTajfa .
2 > tam B KUsbnat;Rsbnwgbnat;b:HrgVg;Rtg; C kat; [AC] Rtg; E nigrgVg;Rtg; F .
eRbobeFobRtIekaN ABC nigRtIekaN BEC . 3 > bgajfa RtIekaN BED nigRtIekaN BFC CaRtIekaNsm)aT .
4 > snt;fa . R)ab;eQaHRtIekaN BFC rYcKNna BF CaGnuKmn_n R .
50(( . kgRtIekaN ABC eKKUsknHbnat;BuH [AD) Edlkat; [BC] Rtg; D . RsaybMePWfa .
51(( . eKeGayABC carwkkgrgVg;Edlmanpit O kaM R Edl AB=c ; AC=b ; BC=a.
RsaybMPWfa . 52(( . eKeGayABC Edl AB=c ; AC=b ; BC=a ehIy r CakaMrgVg;carwkkg ABC.
RsaybMPWfa . 53 . eKeGayRtIekaN ABC nig knHbnat;BuHmMu A kat; [BC]Rtg; D . eKKUsrgVg;kat;tam A Edlb:H [BC] Rtg; D .
k > bgajfa [EF] Rsb [BC] .
x > eRbobeFobRtIekaN AED nig RtIekaN ADC . K > bgajfa AFD nig ABD CaRtIekaNdUcKa .
X > epgpat;smPaB
54 . eKeGayRtIekaNsm)at ABC kMBUl A. KUskMBs; [AH] eKeGay BC = 160mm ; AH = 60mm . edAcMnuc D enAelI [BC] ehIycMnuc E enAelI [BA] Edl BD = 35mm
BE = 56mm . 1> KNna AB nig AC .
2> RbdUcRtIekaN ABC nig RtIekaN BDE . rYcKNna ED
3> bgajfactuekaN ACDE carwkkgrgVg;rYcbBaak;pit .
4> KNna AD rYcbgajfa RtIekaN ACD EkgRtg; A ehIy KNna EC .
55 . eKeGayGgt;Rtg; AB = a nig knHbnat; [Ax) nig [By) Ekgnwg [AB] ehIyenAEtmag
[AB] . elI [Ax) eKedAcMnuc P rYcenAelI [By) eKedAcMnuc Q eday AP = 2 BQ . k> (PQ) kat; (AB) Rtg; S. KNna AS CaGnuKmn_n a .
x> (BP) kat; (AQ) Rtg; M. eRbobeFobRtIekaN MAPnig MQB.
rYcTajfa AM.MB=MP.MQ . K> KNnapleFob nig rYc nig .
X> tam M eKKUsbnat;Ekg [AB] Rtg; H Edlkat; [PQ] Rtg; K . KNna AH g > KNnapleFob nig . rYcbBaak;TItaMgcMnuc M elI [AK] . 56(( . eKeGay [BE] nig [CF] CakMBs;nRtIekaN ABC . enAelI [BE] nig [CF] eKedA cMnuc M nig N Edl .
bgajfaRtIekaN ANM sm)aT .
57 . eKeGayctuekaNBay ABCD man)at [AB] nig [CD] Ggt;RTUg [AC] nig [BD]kat;Ka
Rtg; O. tam O KUsbnat;Rsbnwg)at Edlkat; (AD) Rtg; M nig (BC) Rtg; N .
k > bgajfa .
x > bgajfa O kNal [MN] . K > KNna MN CaGnuKmn_ n a nig b kalNa AB = a ; CD = b .
X > bgajfa .
58((( .enAkgRtIekaN ABC EdlmanmMu ehIycMnuc M CacMnuckNaln [AB] nig [CD] Ekgnwg [AB] Rtg; D .
cUrbgajfa
59 . BIgBagmYy)aneFVIsMNaj;dUcrUbxagsaM I Ggt;EdlPab;kaMBIrtKaCaGgt;RsbKa D 7 J rkRbEvgExS ABCDEFGHIJK 6 6 E Edlt,aj)an H C 5 O 7 5 3 A 4 4
B F
K
G
60 . eKeGayRtIekaN ABC ehIy M ; N ; P kNalerognRCug [BC] ; [AC] ; [AB] . k > RbdUcRtIekaN ABC nig RtIekaN MNP .
x > Rsayfa .
61 . eKeGayrgVg;pit O Ggt;pit . Ggt;F [BC] kat;kNalkaM Rtg; P . k > RbdUcRtIekaN nig RtIekaN .
x > [AH] CakMBs; ehIy M kNal [BC] . bgajfa (AH) // (OM ). K >bnat; kat;kMBs; [AH] Rtg; D . bgajfa
X > RbdUcRtIekaN POM nig RtIekaN OAD .
62 . eKeGayknHrgVg;pit OGgt;pit [AB] . eKKUsbnat; (d) b:HrgVg;Rtg; A . eKedAcMnuc C
enAelI (d) eday AC = 3 cm ehIykaM OA = 2cm . k > KNnaRbEvg OC ; BC .
x > (BC) kat;rgVg;Rtg; D . RbdUc nig rYcTaj .
K >KUskMBs; [AH] n . RbdUc nig rYcTaj .
X > (AH)kat; [BC] Rtg; N nigrgVg;Rtg; M . RbdUc nig .
g > RsaybBaak;factuekaN AHDC carwkkgrgVg; .
63((. kgRtIekaN ABC EdlmanmMu eKKUsknHbnat;BuH [BD)nig [CE) kat;KaRtg; I .
k > bgajfactuekaN ADIE carwkkgrgVg; . x > RsaybBaak;fa ID = IE .
K > RsaybMPWfa .
64( . KNnakaMrgVg;carwkkgctuekaNBaysm)at ABCD EdlmanRbEvg)at 6 cm nig 10 cm. 65 . eKeGayctuekaNBay ABCD EdlGgt;RTUg nigGgt;RTUg
Ggt;RTUg [AC] kat;Ggt;RTUg [BD] Rtg; E .
k > bgajfa .
x > eKeGay AB = 6,5cm ; BC = 25cm ; AD = 39 cm . KNna AC nig BD . K > bgajfactuekaN ABCD carwkkgrgVg;EdlrtUvbBaak;pit O .
X > RbdUcRtIekaN CED nig RtIekaN AEB .
66 . eKeGayctuekaNBay ABCD mYyman . k > bgajfa [CD] Ekgnig [AD] x > rkRbePTctuekaN ABCD .
K > snt; AD = AB . rkRbePTRtIekaN BCD .
67( .eKmanrgVg;BIrmanpit O nig I kat;KaRtg; A nig B EdlrgVg;pit O kat;tam I ehIyrgVg;pit I kat;tam O . tam A KUsbnat;mYykat;rgVg;pit O Rtg; M nigrgVg;pit I Rtg; N . RsaybBaak;faRtIekaN AOI ; BOI nig BMN CaRtIekaNsmgS .
68( . eKmanrgVg;BIrmanpitmanpitrYm O man kaM R nig 2R . bnat;b:HrgVg;xagkgRtg; M kat;rgVg;xageRkA Rtg; A nig B . bnay (OM) kat;rgVg;xageRkARtg; C . RsaybMPWfa RtIekaN AOC nig BOC CARtIekaNsmgS .
69 . eKmanrgVg;BIrmanpit O nig I kat;KaRtg; A nig M . P kNal [OI] tam A KUsGgt;mYy
Ekgnwg [PA] kat;rgVg;TaMgBIrRtg; C nig B. E nig D CacMenalEkgn O nig I elI [BC] .
RsaybMPWfa AB = AC .
70 . RtIekaN ABC carwkgrgVg;pit Oman M kNalFtUc AC. KUsGgt;F [NM]Rsb [AB] .
RsaybMPWfa
71(( . eKeGayRtIekaN ABC mYyman mMu A CamMuTal . emdaTrn [AC] kat; [BC] Rtg; D rYcKUsemdaTr [AB] kat; [BC] Rtg; E.
RsaybBaak;fa .
72(( . elI)at [BC] nRtIekaN ABC eKedAcMnuc D mYy . tam M nig N cMnuckNalerog
[BD] nig [DC] eKKUsbnat;mYyEkg nig [BC] kat; [AB] Rtg; E nig [AC] Rtg; F .
RsaybMPWfa
73(.eKeGayRbelLRkam ABCDmYy. KUs [AE]kat; [CD]Rtg;kNalrYckat; [BD]Rtg; O .
RsaybMPWfa .
74(( . kgRtIekaN ABC KUsemdan [AM].tam BKUsknHbnat;mYykat;tamcMnuckNal O n
[AM]rYckat; [AC]Rtg; D.tam MKUsknHbnat;mYyRsbnwg [AD]Edlkat; [AC]Rtg; E. RsaybMPWfa CD = 2 AD 75(( . [AM] CaemdannRtIekaN ABC . elI [BA] eKedAcMnuc E Edl BE = 2 EA .
[CE] kat; [AM] Rtg; O .
1 > bMPWfa O kNal [AM] .
2 > RsaybMPWfa CE = 4 EO . 76 . O CapitrgVg;carwkkgctuekaNBaysm)aT ABCD mankaM r . I nig J CacMnuckNalerog
n [AB] nig [CD] 1 > bgajfaRtIekaN AOD CaRtIekaNEkg Rtg; O .
2 > Tajfa ( H CaeCIgcMenalEkgn O elI [AD] ) . 3 > KNna AB nig CD ebI AB = 4 CD . (qmas vi >bwgRtEbk 2003 ) 77 . eKeGayrgVg;mYypit O kaM R = 2,5 cm . rYceKKUsGgt;F [EF] Edl EF = 4 cm ehIysg;Ggt;pit [EM] rYcKUs [FI] Ekg [EM] Rtg; I .
k > R)ab;eQaHRtIekaN EFM rYcKNna FM ; EI . ( qmas vi>RBHyuKnr 2003 ) x bnat;b:HrgVg; ( O ) Rtg; M kat; (EF) Rtg; X . RbdUc nig . K > TajbBaak;fa rYcKNna MX ; FX .
78 . eKeGayrgVg;pit O nig kaM R edayFbItKa bnat;b:HrgVg; (O) Rtg;
B kat; (AD) Rtg; P . 1 > bgajfa RtIekaN PAB nig PBD CaRtIekaNsm)aT . ( qmas vi> Gnuvt 2005 ) 2 > KNna PO nig PB CaGnuKmn_n R .
3 > tam B eKTMlak;cMenalEkgelI [AD] Rtg; H nigbnay (CD) kat; (PB) Rtg; M .
RbdUcRtIekaN PHB nig RtIekaN PMD rYcTajfa PD.PH = PB . PM .
79 . eKeGayctuekaNBay ABCD EkgRtg; A nig B.Edl DA = DCnig I kNal [AC ] . 1 > RbdUc nig .
2 > RsaybBaak;fa ( qmas vi > bwgekgkg 2004 ) 80 . eKeGayrgVg;pit O kaM R ehIymanGgt;pitBIr [AB] nig [CD] EkgKa . E CacMnuckNaln kaM [OC] . bnat; (AE) kat;rgVg;Rtg; F .
1 > eRbobeFobRtIekaN AOE nig ABF . ( qmas vi > vtekaH 2003 ) 2 > RsaybBaak;fa .
3 > bgajfactuekaN OEFB carwkkgrgVg;EdlRtUvbBaak;pit I rbs;va. 4 > KNnapleFobRkLapnRtIekaN AOE nig AFB .
81 . eKeGayrgVg;pit O Ggt;pit AB = 2 R . eKedAcMnuc M enAelIrgVg; Edl AM< R .
KUsrgVg;pit M kaM [AM] kat;rgVg;FM Rtg; I . eKKUsGgt;pit [AC] nrgVg;tUc .
1 > RsaybMPWfa cMnuc C ; I ; B rt;Rtg;Ka .
2 > bgajfa RtIekaN ABC sm)at ( qmas vI>bwgRtEbk 2004 )
3 > RbdUc nig rYcTajfa
82 . eKeGayrgVg; C(O;R) Ggt;pit [BD] . F CacMnucmYyenAelIrgVg;edayF .
bnat;b:HrgVg;Rtg; F CYb (BD) Rtg; E .
1 > R)ab;eQaH rYcKNna OE nig EF CAGnuKmn_n R .
2 > eRbobeFob nig rYcTajfa .
3 > bnat;b:HrgVg;Rtg; D CYb [EF] Rtg; M . bgajfa . 4 > RsaybMPWfa . ( qmas vi > samKI 2004 ) 83 . eKeGayrgVg;pit O . KUsbnat; ( D) b:HrgVg;Rtg; P . A CacMnucmYynbnat;b:H (D) rgVg;Ggt;pit [OA] kat;knHbnat;BuHmMu OAP Rtg; H . bnay (OH) kat; (D) Rtg; M .
k > bgajfargVg;Ggt;pit [OA] kat;tamcMnuc P .
x > R)ab;RbePTRtIekaN AOM .
K > bnat; (OA) kat;rgVg;pit O Rtg; E nig F . RbdUc nig .
X > bgajfa . ( qmas vi > pSaredImfv 2004 ) 84 . manRtIekaNsmgS ABC carwkkgrgVg; (O) . M CAcMnucmYyenAelIFtUc AB elI [CM] edAcMnuc D Edl MD=MA .
1 > RsaybMPWfa CaRtIekaNsmgS . 2 > bnat; (MA) nig (BC) kat;KaRtg; E . RbdUc nig .
3 > TajbBaak;fa ( qmas vi > bwgekgkg 2006 ) 85 . eKeGaybnat; (D) b:HrgVg;pit O Rtg;cMnuc M . A CacMnucmYynbnat; (D) ehIy I CacMnuckNaln [AO] . k > bgajfa .
x > N CacMnuckNalnF OM rbs;rgVg;pit I ehIy [ON) kat;bnat; (D) Rtg; P .
a . bgajfa [AN) CaknHbnat;BuHn
b . R)ab;RbePTRtIekaN AOP K > (OA) kat;rgVg; O Rtg; J nig K . ( qmas vi > TYlTMBUg 2006 ) RbdUc nig rYcTajfa . 86 . eKeGayrgVg;pit O Ggt;pit [AB] . eKKUsbnat;b:H (xy) eTAnigrgVg;Rtg; A . C CacMnuc
mYyenAelIrgVg; ehIy D nig E CacMenalEkgncMnuc C elI [AB] nig elI (xy) . ehIy M CacMnuckNal [DE] . 1 > bBaak;RbePTRtIekaN AMO . 2 > eKKUsbnat;b:HrgVg;pit O Rtg; C Edlkat; (xy) Rtg; F .
bgajfa [CA) CaknHbnat;BuHnmuM OCE nigmuM DCF .
3 > bgajfa dUc .
4 > TajbBaak;fa ( qmas vi > pSaedImfv 2005 ) 87 . tamcMnuc M enAeRkArgVg;pit O eKKUsbnat;BIrb:HrgVg;Rtg; A nig B . bnat;EdlEkgnig [OB] Rtg; O kat; [MA] Rtg; S .
k > rkRbePTctuekaN OBMS .
x > bgajfa SO = SM .
K > bnat; (MA) nig (BO) RbsBVKaRtg; I . RbdUc nig rYcKNna . X > bgajfa . ( qmas vi > c,arGMeBA 2005 ) 88 . egVg;pit O nig I kat;KaRtg; A nig B . bnayGgt;pit (AC)nrgVg; (O) kat;rgVg; ( I ) Rtg;
E nig bnaynGgt;pit (AD) nrgVg; ( I ) kat;rgVg; ( O ) Rtg; F .
1 >eRbobeFob RtIekaN ACF nig RtIekaN ADE rYcTajfa AC.AE = AD.AF .
2 > bMPWfa B enAelI [CD] nigfa [AB] CakMBs; RtIekaN ACD .
3 > [CF) kat; [DE) Rtg; P . bgajfa ctuekaN AEPF carwkkgrgVg; .
4 > bMPWfa P ; A ; B rt;Rtg;CYr . ( qms vi > c,aGMeBA 2006 ) 89 . eKeGayRtIekaNsmgS ABC nig O CapitrgVg;carwkeRkARtIekaNenH. eKykcMnuc M enAelI (BA) nigcMnuc N enAelI (AC) Edl BM = AN .
k > eRbobeFobRtIekaN OBM nig RtIekaN OAN rYcTajvi)ak .
x > RsaybBaak;factuekaN AMON carwkkgrgVg; . K > bgajfa RtIekaN MON sm)aT rYcKNnamuMrbs;va .
X > eKsg;RbelLRkam MAPN. [OA]kat; [MN]Rtg; I nigbnayn (MP)Rtg; K .
eRbobeFobRtIekaN IAN nig RtIekaN IKM . ( qmas vi bwgRtEbk 2005 ) 90 . eKeGayrgVg; (O ; R)Ggt;pit [AB]. KUsGgt;F [AM] eGay)an MC = AM. tam A KUsbnat; eGayEkgnwg [AM] vakat;rgVg; nig bnat; (CB) Rtg; I nig E .
k > bgajfa RtIekaN ABC sm)aT .
x > Rsayfa B kNal [CE] rYc bgajfa CA.AB = AM.CE K > cUreRbobeFob nig ( qmas vi )ak;TUk 2005 ) 91 . eKeGayRtIekaNEkgsm)aT ABC eday AB = AC = a . ehIyDACkCaRtIekaN Ekg
sm)aTkMBUl D . RtIekaNTaMgBIrenAsgxagRCugrYm [AC] .
k > kMnt;RbePTctuekaN ABCD rYc KNna BC ; AD nig BD CaGnuKmn_n a .
x > Ggt;RTUg [AC]kat; [BD] Rtg; O. KNna OA ; OB ; OC ; OD CaGnuKmn_n a .
K > RbdUcRtIekaN AOD nig RtIekaN BOC rYcKNnapleFobdMNUc .
X> rgVg;Ggt;pit [BC] kat; (BD) Rtg; K . bgajfa [CK] CakMBs;RtIekaN BCD . KNna DK nig KO . (RblgsBaabRt qaM 1995nigqmas vi > TYlTMBUg 2005 ) 92 . eKrGayrgVg;pit O Ggt;pit [AB]. bnat;Ekg [AB] Rtg; H n [OB] kat;rgVg;Rtg; C nig
D nig I CacMnuckNaln [CH] . bnat; (AI) kat;rgVg;Rtg; M . bnat;b:HrgVg;Rtg; M kat;
[CD] Rtg; N .
1 > bgajfa RtIekaN NIM sm)aT . ( qmas vi > TYlTMBUg 2004 ) 2 > bgajfa [MA) CaknHbnat;BuHn CMD .
3 > eRbobeFob IMD nig CMA rYcTajfa MA.MI=MC.MD . 93 . eKeGayRtIekaN ABC EkgRtg; A .
k > KNna AB edaydwgfa BC = 20 cm nig . x > KNna BC edaydwgfa AC = 5 cm nig . 94 . eKeGayRtIekaNEkgsm)aT ABC Edl nig CakMBs; . k > KNna AH CaGnuKmn_n .
x > O CapitrgVg;carwkkgmanmaM . bgajfa O enAelI [AH] .
K > KNna OA CaGnuKmn_n r .
X > KNna r CaGnuKmn_n a . ( RblgsBaabRtqaM 2000 )an 30 Bin ) 95 . rgVg;pit O mYymanGgt;pit [AB] Edl AB = 5 cm. bnat; ( L) b:HrgVg; (O) Rtg;cMnuc C ehIyEdl AC = 4 cm . bnat; (AD) CYbrgVg; (O) mgeTotRtg; D ehIyEkgnwg (L) Rtg; E.
MCacMnucRbsBVrvag (AC) nig (BD) . N CAcMnuckNal [AD] .
1- kMNt;RbePTnRtIekaN ABC nig RtIekaN ABD . KNnabrimaRtnRtIekaN ABC .
2- bgajfa CENO CactuekaNEkg .
3- eRbobeFobRtIekaN MAB nigRtIekaN MDC rYcTajfa MA.MC = MB.MD . ( RblgsBaabRt qaM 2006 )an 25 Bin ) 96 . ABC CaRtIekaNsmgScarwkkgrgVg;pit O. AB =AC=BC =2cm . eKKUsrgVg;Ggt;pit [AD] Edlkat; [BC] Rtg; H .
1 > KNna AD nig BD ( eKeGay ) 2 > RbdUcRtIekaN BHD nig AHC . rYcKNnapleFobdMnUc .
3 > yk K CacMnuckNaln [BD] . bnat; (HK) kat;RCug [AC] Rtg; I .
bgajfa [IK] Ekgnwg [AC] . ( RblgsBaabRt qaM 2005 )an 30Bin ) 97 . kgrgVg;pit O mYymanGgt;FBIrminb:unKa [AB] nig [CD] EdlEkgKaRtg;cMnuc I .
M CacMnuckNalnGgt; [BD] . bnat; (MI) CYbGgt; [AC] Rtg; N .
1 > bgajfa RtIekaN MBI nig RtIekaN MDI CaRtIekaNsm)aT .
2 > eRbobeFobRtIekaN IBD nig RtIekaN NCI . TajbBaak;fa . 3 >eKyk IA = a ; IC = b . KNna AC nig IN eGayCab;Tak;Tg a nig b .
( RblgsBaabRt qaM 2004 )an 25 Bin ) 98 . ekaN manmaD nigmankMBs; . ekan manmaD nig
mankMBs; . ekan nig ekan CaekanEdldUcKa. ( ebkCnmin)ac;KUrrUbeT ) KNnakMBs; nekan .
( RblgsBaabRt qaM 2003 )an 10 Bin ) 99 . eKmanRtIekaN ABC EkgRtg; A ehIyman AB=3cm; AC = 4cm . rgVg; mYymanGgt; pit [AB] ehIyCYb [BC] Rtg; H .
1 > bgajfa [AH] CakMBs;nRtIekaN ABC rYcKNna BC nig AH .
2 > rgVg; mYyeTotcarwkeRkARtIekaNEkg AHC . M CacMnucmYyenAelIFtUc CH . bnat; (CM) CYbbnat; (AH) Rtg; N .
eRboeFobRtIekaN MAN nig RtIekaN HCN rYcTajfa AM.HN = MN.CH ( RblgsBaabRtqaM 2003 )an25Bin ) 100 . MCacMnucmYyenAelIrgVg; Edlmanpit O kaM R. rgVg;Edlmanpit MkaM r(Edl R>r ) CYbrgVg; Rtg; A nig B . bnat; (OM) CYbrgVg; Rtg; D ehIyCYbrgVg; Rtg; E nig F Edl . bnat; Ekgnwg (DM) Rtg; F ehIyCYbbnat; (DA) nig (DB) erogKaRtg;
cMnuc I nig J . 1 > KNnargVas;mMu nig . Tajfabnat; (DI) nig (DJ)b:HrgVg; Rtg; Anig B.
2 > bgajfa ctuekaN AMFI carwkkgrgVg;mYy . 3 > eRbobeFobRtIekaN ADM nig RtIekaN FDI .
4 > TAjbBaak;fa ehIy
( RblgsBaabRt qaM 2002 )an 30 Bin ) 101 . rgVg;mYymanpit O kaMRbEvg 4cm nigGgt;pit [AB] . H CacMnuckNal n [OB] .
bnat;mYyEkg [AB] Rtg; H ehIyCYbrgVg; (O) Rtg; M nig N . (AN) nig (BN) CYbKaRtg; I . 1 > cUrKNnargVas; MA nig MB .
2 > cUreRbobeFobRtIekaN ABI nig RtIekaN NMI . ( RblgsBaabRt qaM 2001 )an 30Bin ) 102 . ABC CaRtIekaNsmgS . G CacMnucmYyenAelI [AB] rgVg;pit A kaM [AG] kat;bnay (AB) xag A Rtg; D nig kat; [AC] Rtg; E bnat; (DE) kat; (BC) Rtg; F . 1 > KNna rYcbgajfa RtIekaN FBD CaRtIekaNEkgRtg; F .
2 > eRbobeFobRtIekaN DEG nig RtIekaN EFC . (RblgsBaabRt qaM 1999 )an 30 Bin ) 103 . ABCD CactuekaNBayEkg Edlman nig DA=DC . I kNal [AC] . k > RbdUcRtIekaN ABC nig DIC .
x >RsaybMPWfa (RblgsBaabRt qaM 1998 )an 30 Bin ) 104 . eKeGayrgVg;pit O Ggt;pit [AB] nig cMnuc P enAeRkArgVg;enH . bnat; (PA) nig (PB) kat;rgVg;erogKaRtg;cMnuc M nig N enAmagn (AB) .
1 > RsaybBaak;fa [AN] nig [ BM] CakMBs;nRtIekaN PAB .
2 > H CacMnucRbsBVrvag [AN]nig [MB] . RsaybBaak;fa [PH] Ekgnwg [AB] .
3 > bgajfactuekaN HMPN carwkkgrgVg;mYy .
4 > RsaybBaak;fa AN.BP=BM.AP . ( RblgsBaabRt qaM 1996 elIkTI 1 )an50Bin ) 105 . eKeGayrgVg;pit O kaM R . KUsbnat; (D) b:HrgVg;Rtg; P . A CacMnucmYyn (D) . rgVg;Ggt; pit [OA] kat;knHbnat;BuHOAP Rtg; H . bnay (OH) kat; (D) Rtg; M .
1 > bgajfargVg;Ggt;pit [OA] kat;tamcMnuc P . 2 > R)ab;RbePTRtIekaN AOM .
3 > KUskMBs; [MK] nRtIekaN AOM . Rsayfa MK = R . ( RblgsBaabRtqaM 1993 ) 106 . eKeGayrgVg; (C) pit O viCmaRt [AB] Edl AB = 4 R nigrgVg; (I) viCmaRt [OA] . tam B eKKUsbnat;b:H (BM) rTAniwrgVg; (I) Rtg; M . (BM) kat;rgVg; (C) Rtg; E .
1 > bgajfa (AE) Rsbnwg (IM) . rYcTajfa [AM) CabnHbnat;BuHmMu BEA . 2 > bnat; (AM) kat; (BM) Rtg; N . bgajfa M kNal [AN] .
3 > (ON) kat; (BM) Rtg; G . etI G CaGVIcMeBaH ABN ? KNna OG CaGnuKmn_n R
4 > bnat; (AE) kat; (BN) Rtg; P . bgajfa (MP) Ekgnwg (AB) .
( RblgsBaabRtqaM 1991 ) 107 . rgVg;BIrmanpit nig mankaM nig b:HKaxageRkARtg; . bnat;mYyKUsecjBI
kat;rgVg;enHRtg; nig . 1 > bgajfa nig RsbKa .
2 > RsaybMPWeGayeXIjfabnat;b:HrgVg;Rtg; nig RsbKa .
3 > KNnapleFob CaGnuKmn_n nig. ( qmas vi > bwgRtEbk 2005 ) 108 . eK[RtIekaN ABC EkgRtg; A mankMBs; [AH] .
1 > KNna BC nig AH ebIeKdwgfa AB = 6cm ; AC = 8 cm .
2 > rgVg;Ggt;pit [AH] Edlkat; (AB) Rtg; P nig (AC) Rtg; Q . R)ab;eQaHctuekaN APHQ 3 > Rsayfa AQP nigABC dUcKa rYcKNnatMlpleFobdMnUc . 4 > KNnaRkLapRtIekaN AQP . ( qmas vi > vtekaH 2006 )an 35 Bin ) 109 . eKeHayrgVg;pit O Ggt;pit AB = 2R . C CacMnucmYyenAelIrgVg;Edl BC = R bnat;b:HrgVg;
Rtg; A kat;bnay (BC) Rtg; D . (CH) CacMenalEkgncMnuc C elI (AB) .
1 > KNna AC ; CH ; AH CaGnuKmn_ n R .
2 > RbdUcRtIekaN ABC nig RtIekaN ABD rYcTajvi)ak .
3 > edA I enAelI [BD] Edl BI = 2 IO . bgajfa (OI)//(AD) rYcTAjfa AD = 2 IO . 4 > K kNal (AD) . bgajfa RtIekaN AKC smgS .
110 . eKeGayrgVg;pit O Ggt;pit [BC] Edl BC = 2R . Cabnat;b:HrgVg; O Rtg;cMnuc B .
M CacMnucmYyenAelIbnat; Edl . (CM) kat;rgVg; O Rtg; A . Ggt;F [AD] Ekgnwg [BC] Rtg;cMnuc H .
1 > R)Ab;eQaHRtIekaN ACD .
2 > RbdUc ABC nig AMB rYcKNna CM nig AB CaGnuKmn_n R . 3 > KNna BH ; CH ; AH CaGnuKmn_n R rYc KNna ?
( qmas vi > TYlTMBUg 2006 ) 111 . tamkMBUl A nRtIekaNsm)aT ABC eKKUsbnat;mYyEdlkat; [BC] Rtg; E
nigkat;rgVg;carwkeRkAenHrtg; F .
1 > eRbobeFobRtIekaN ABE nig AFB rYcTajbgajfa .
2 > bnat;KUsecjBIcMnuc C Ekg [AF]Rtg; Hkat; (BF)Rtg; I. bgajfa (FA)CaemdaTrn[CI] . 3 > eKbnay (CA) eGay)an AD=AC bgajfactuekaN CBID carwkkgrgVg;mYy rYcbBaak;pit.
4 > eK]bmafa AC = 6cm ; . KNna RkLapRtIekaN AIC .
( qmasvi RBHsIusuvti 2006 ) 112 . eKeGayctuekaNBayEkg ABCD man)attUc AB = 3cm )atFM CD=5cm nig AD=4cm .
k > KNna BC x > rYcbgajfa RtIekaN BDC sm)aT
K > bnat;KUsBI B Ekgnwg [CD] Rtg; E nig yk I kNal [BC] . bgajfa A ; I ; E ; D ; B enAelIrgVg;EtmYy . X > bgajfaRtIekaN AID nigRtIekaN BDC dUcKa . g > [AI) kat; [BE) Rtg; K . Rsayfa [AI) CaknHbnat;BuHnmuM BAE c > KNna KB nig EK . 113 .tagnigCargVas;RCugTaMgBIrnmMuEkgrbs;RtIekaNEkgmYy.CargVas;kMBs;cMeBaHGuIb:Uetnus RsaybMPWfa
114 . eKmanRtIekaN ABC EkgRtg; A eday AB =5cm ; AC = 8 cm . tamcMnuc M n [AB] eKKUsbnat;Rsbnig [AC] Edlkat; [BC] Rtg; N . eKyk BM = x ( cm) . k > KNna MN CaHnuKmn_n x .
x > KNnaRkLapRtIekaN BMN CaGnuKmn_ n x . K > KNnaRkLapctuekaN AMNC CaGnuKmn_n x . X > KNna x ebI RkLapctuekaN AMNC esIRtIKuNRkLapRtIekaN BMN .
115 . elIbnat; (D) eKedAbIcMnuc O ; A ; B Edl rYcsg;rgVg; . P CacMnucmYyenAelIrgVg; ehIyenAelIGgt;pitEdlekgnwg (D) .
1 > KNna AP ; PB CaGnuKmn_n .
2 > eRbobeFobpleFob nig .
3 > M CacMnucmYycltenAelIrgVg; (O) nig
k > RbdUcRtIekaN OMA nigRtIekaN OMB .
x > etIpleFob ERbRbYlbeT ? kalNa M rt;enAelIrgVg; ( C ) .
116 . enAelIbnat; (xy) eKkMnt; AC=BC=a Rtg;cMnuc C eKKUsbnat;Ekgnwg (AB) ehIyenAelI
bnat;EkgenH eKedAcMnuc M Edl . eKsg;rgVg;Ggt;pit [AB] Ggt;pit [AM] kat;rgVg; Rtg; D . H CacMenalEkgn D elI [AB] .
1 > RsaybMPWfa RtIekaN ACM RtIekaN ADB nig RtIekaN HAD dUcKa .
2 > RsaybMPWfa k > x > K >
3 > KNna AM ; AD ; BD ; AH ; BH ; DH . 117 . eKmankaer ABCD EdlmanRCug a nig M kNal [BC]. AM) kat; (CD)Rtg; N ehIybnat;
Ekg (AM) Rtg; A kat; (BC) nig (CD)Rtg; P nig Q . 1 > bgajfa . 2 > RsaybMPWfa . 3 > bgajfa RtIekaN AMQ sm)aT nig KNna rgVas;RCugrbs;va .
4 > RsaybBaak;factuekaN ACMQ carwkkgrgVg;mYy . 118 . eKeGaybnat; Rtg; O . Edl eKKUsmMuEkg Edl
nig kat; Rtg; nig . 1 > RsaybMPWfa . 2 > KUs nig . kMnt;eQaHctuekaN OEAF rYcRsayfa .
3 > RbdUcRtIekaN AEF nig RtIekaN ABC .
4 > snt; . KNna OB ; EA nig OE CaGnuKmn_n a .
119(( . eKeGay kaer ABCD EdlRCugmanrgVas;esI 1 cm . enAelIRCug [BC] eKedAcMnuc E eday .
RsaybMPWfa [AE) CaknHbnat;BuHnmMu BAC .
120 ((. tamcMnuc I enAeRkArgVg;pit O eKKUsbnat;b:H (IA) nig (IB) Edlb:HrgVg;Rtg; A nig B .
tam I dEdleKKUsbnat;mYykat;rgVg; Rtg; E nig F . (AE) kat; (IB) Rtg; M .
RsaybBaak;fa M kNal [OB] .
121( .eKeGayctuekaesIRCugmanrgVas; .nigCakaMrgVg;carwkeRkA nig.
RsaybBaak;fa
122((( . enAelI nig EdlCakMBs;n eKedAcMnuc nig erogKaEdl
.
1. RbdUc nig rYcTajfa
2. RsaybMPWfa sm)at .
123 . KNnaplbUk = ?tamrUbxageRkam A B
C
E D
124 . eKeGayRtIekan manrgVas;RCug nig mMu . RsaybBaak;fa RkLapRtIekaN KW
125(( . eKeGayRtIekaN man .
RsaybBaak;fa .
126 . eKeGaybIcMnYn CargVas;RCugnRtIekaN . ehIyepgpat;TMnak;TMng;
.
R)ab;RbePTRtIekan .
127 . eKeGayctuekanEkg mYy . CacMnucmYyenAxagkgctuekanEkg
ehIyEdl .
cUrRsaybMePwfa
128 . kgrUbxagsaM ebI B C dWeRk A D KNna G
E
F
129 . eKeGayrgVg;pit OmankaM R. KUsGgt;pitBIrEkgKa [AB]nig [CD].KUsGgt;F[AM]kat;
[OC]Rtg; N ehIypMnig [AB] )an . 1> KNna MB nig AM CaGnuKmn_n R .
2> RbdUcRtIekaN AON nig RtIekaN ABM rYc KNna ON nig AN .
3> bgajfaRtIekaN OBM smgS . ( qmas I extRBEvg 2005 ) 130 . eKeGayRtIekaN ABC EkgRtg; A Edl BC = 2a . k > KNna AB ; AC CaGnuKmn_n a .
x >eKKUsknHrgVg;viCmaRt [AC]Edlminkat; [BC].edAcMnuc DenAelIknHrgVg;eday
RbdUc nig . rUcTajfa .
K >CakMBs;n. KNna AH CaGnuKmn_n a rYceRbobeFob AH nig AD . ( qmas vi RBHyuKn 2006 ) 131 . eKeGayctuekaNBay ABCD Ekg Rtg; A nig D . bgajfa ebI [AC] CamFmsmamaRtevag )at [AB] nig [CD] enaHeK)an [AC] Ekg [ BC] . 132 eKeGay RtIekaNsmgS ABC Edl AB=BC=AC=2cm ehIycarwkkgrrgVg; O.
eKKUsGgt;pit [AD] Edlkat; [BC] Rtg; H . k > KNnargVas;RCug AD nig BD .
x > RbdUcRtIekaN BDH nig RtIekaN ACH rYcKNnapleFobdMnUc . ( vi > vtPM 2006 ) 133 . M CacMnuckNalRCug [BC] nRtIekaN ABC mYy snt; .
k > bgajfa RtIekaN ABM nig RtIekaN CBA CaRtIekaNdUcKa .
x > bgajfa . eRbobeFob BC eTAnwgGgt;RTUgkaerEdlmanRCug [AB] . K > yk I CaeCIgnknHbnat;BuHmMukg BAC enAelI [BC] nig J CaeCIgnknHbnat;BuHmMukg
AMB enAelIRCug [AB] . bgajfa [IJ] Rsbnig [AC] . ( qmasext kNal 2006 ) 134 . KNna HD ; AD ; AB : AH nig BC kgrUbxageRkam B H 4 A D 2 C 134 . manrgVg;pit O viCmaRt [AB] . tamcMnuc A eKKUsbnat;mYykat;rgVg;Rtg; M nigkat;bnat;b:H
rgVg;Rtg; B enH Rtg; C . I CacMnuckNal [AM] .
k > R)ab;eQaH RtIekaN AIO .
x > RbdUcRtIekaN AIO nig RtIekaN ABC .
K > ebI BC = 6cm ; . KNna AB .
X > KNnaRkLapnctuekaN OICB . ( qmas Gnuvi ctumux ) 135 . manrgVg;pit O kaM R Ggt;pit [AB] . KUsbnat;b:HRtg; A tam M enAelIbnat;b:HenH KUs [BM] kat;rgVg;Rtg; C .
k > RbdUcRtIekaN ACM nig RtIekaN ABc rYcTajfa AB.AC=AM.BXC x > KUsbnat;b:H (MD) b:HrgVg;Rtg; D. RsaybMPWfa cMnuc A ; O ; D ; M enAelIrgVg;EtmYy. K > RsaybMPWfa
X > eKeGay BC= 6 ; CM=3 . KNna AB nig AM .
136 . manrgVg;pit O kaM R Ggt;pit [AB] . M CacMnucmYyenAkgrgVg; bnat; (AM) nig (BN) kat;rgVg; Rtg;cMnuc C nig D .
1 > RbdUcRtIekaN ADM nig RtIekaN BCM rYcTajpleFobdMnUc . 2 > bgajfa .
3 > bnat; (D) b:HrgVg;Rtg; B kat; (AC) Rtg; E . ebI .
KNna BE ; AE ; BC CaGnuKmn_n R . ( qmas vi \neTvI 2005 ) 137 . enAelIbnat;mYyeKedAbIcMnuc A ;B ;C ; tamlMdab;enHeday AB=2a ; BC = a .
eKKUsrgVg;mYymanGgt;pit [AB] nig ( d) Ekgnig (AC) Rtg; C . tamcMnuc A KUsbnat;mYy
kat;rgVg; Rtg; D nig (D) Rtg; E . 1 > RbdUcRtIekaN ADB nig RtIekaN ACE .
2 > KNnaplKuN AD. AE CaGnuKmn_n a .
3 > (DB) CYb (D) Rtg; F nig (EB) CYb (AF) Rtg; H . bgajfa (EB) (AF) Rtg; H .
4 > RsaybBaak;fa cMnuc E ;D ;H nig F enAelIrgVg;EtmYy . ( qmas vi vtPM 2004 ) 138 . eKeGayRtIekaN ABC Edlman [AH] CakMBs;nig . k > KNna AH ; AC . x > rgVg;Ggt;pit [AH] kat; (AB) Rtg; M nig (AC) Rtg; N . KNna AM ; AN .
K > bgajfa .
X > RbdUcRtIekaN ABC nig RtIekaN ANM rYcTajfa .
139 . eKeGayRtIekaN ABC Edlman [AH] CakMBs; nig. k > KNna AH ; BH ; CH ; AC .
x > rgVg;Ggt;pit [AH] kat; (AB) Rtg; D nig (AC) Rtg; E . KNna AD ; AE .
K > RbdUcRtIekaN ABC nig RtIekaN AED rYcKNna DE . 140 . manrgVg;pit OGgt;pit [AB] . eKKUsGgt;F [CD] EkgkaM [OA] Rtg; H . 1 > KNna rYc AH nig BC ebI AB = 8 cm nig OH = 2,5 cm .
2 > eKKUsGgt;F [CP] Ekgnwg [CD] Rtg; C . bgajfacMnuc D ; O ; P rt;Rtg;Ka .
3 > bnat;b:HrgVg; O Rtg; D kat; (AB) Rtg;cMnuc E .
RbdUcRtIekaN EDA nig RtIekaN EBD rYcbgajfa . 141.manRtIekaN ABC mYyEdlman AB = 4cm ; AC= 6cm. MCacMnucmYyenAelI [AB] nig N
enAelIbnayRCug (AC) Edl BM = 2cm ; CN= 3 cm .
1 > rkRbePTctuekaN MBCN .
2 > KUsrgVg;pit O Ggt;pit [AB] nigrgVg;pit I Ggt;pit [AC] kat;KaRtg; H .
k > bgajfa [AH] CakMBs;nRtIekaN ABC .
x > KNna ebI BH = 2cm .
3 > KUsGgt;F [HD] Ekg [AB] Rtg; I rYcKUsGgt;F [DE] Rsbnwg [AB] .
bgajfacMnuc H ; O ; E rt;Rtg;CYr .
4 > RbdUcRtIekaN BHI nig RtIekaN EHA . ( qmas vi > c,aGMeBA 2004 ) 142 . manrgVg;pit O kaM R Ggt;pit [CD] . tamcMnuc B mYyenAeRkArgVg; eKKUs [BC] nig [CD] tat;rgVg;Rtg; A nig E . [AD] kat; [EC] Rtg; I .
k > bgajfa [BI] Ekgnwg [CD] Rtg; H .
x >RsaybBaak;fa . K > tamcMnuc HKUs [HM]Rsb [AD] Edlkat; [BC] Rtg; M. Rsayfa CM.HM=CH. MA 143 . eKeGayRtIekaN ABC Ekg Rtg; A . man [AH] CakMBs; .
k > RbdUcRtIekaN ABC RtIekaN ABH nig RtIekaN ACH .
x > TajbBaak;fa a .
b .
c .
K > RsaybMPWfa a . b .
c . d .
144 . eKeGayrgVg;pit O Ggt;pit [AB] nig bnat; (D) Cabnat;b:HrgVg;Rtg; A . M CacMnucmYyenA
elIrgVg; P CacMenalEkgn M elI [AB] . Q CacMenalEkgn MelII (D)ehIy I CacMnuckNal [PQ] . bnat;b:HrgVg; O Rtg; M kat; (D) Rtg; T .
k > R)ab;eQaHctuekaN APMQ nig RtIekaN AIO .
x > bgajfa [AM) CaknHbnat;BuHnmMu QMO nig TMP .
K > RbdUcRtIekaN AIQ nig RtIekaN ATM .
X > KNnargVas; QA ebI QP=10cm nig
145 . eKeGayrgVg;pit O kaM R Ggt;pit [AB]. enAelIbnat; (D) b:HrgVg;Rtg; A eKedAcMnuc M mYy
eday . [MB] kat;rgVg; Rtg; C .
a . RsaybMPWfa RtIekaN ABC dUc RtIekaN AMB .
b . KNna BM CaGnuKmn_n R nig rgVas;muM AOM .
c . rksMnMucMnuc I kNal [OM] kalNa M rt;elIbnat; (D) . 146 . eKeGayrgVg;pit OBIcMnuc AmYyenAelIrgVg;eKKUsGgt;FBIr[AB]nig[AC]enAmagnGgt;KUs
ecjBIA. bnat;b:HrgVg;Rtg; A nigCkat;KaRtg; S. Ggt;RTUgmYyEkgnwg[AB]kat; [BC]Rtg; T . k > RsaybMPWfa RtIekaN SAC nig RtIekaN TAB sm)aT . x > RbdUcRtIekaN SAC nig RtIekaN TAB .
K > RsaybMPWfa cMnuc A ; S ; C ; T ; O sitenAelIrgVg;EtmYy .
X > bgajfa [ST] Rsbnig [AB] .
147 . eKeGayRtIekaN ABC EkgRtg; A nig [AH] CakMBs; Edl AC = a ; . a . KNna HB HC nig .
b . I kNal [BC] . R)ab;eQaHRtIekaN AIB rYcKNna AI .
c . O kNal [BC] . R)ab;eQaHctuekaN OICA .
d . rgVg;Ggt;pit [AB] nig [AC] kat;KaRtg; N . Rsayfa cMnuc N RtYtelI H enAelI [BC] . 148 . eKeGayrgVg;pit OGgt;pit [AB] Edl AB=4R nig rgVg;pit I Ggt;pit [OA] . tam B eK
KUsbnat;b:H (MB)eTAnigrgVg; ( I ) Rtg; M . bnat; (BM) kat;rgVg; (O) Rtg; E .
1 > bgajfa (EA) Rsb (IM) rYcbBaak;fa [AM) CaknHbnat;BuHn BAE .
2 > (AM) kat;rgVg; (O0 Rtg; N . bgajfa M kNal [AN] . 3 > (ON) kat; (BM) Rtg; G. etI GtagGVIcMeBaHRtIekaN ANBrYcKNna OG CaGnuKmn_n R.
149 . eKmanrgVg;pit O Ggt;pitBIr [AB] nig [CD] minEkgKa. eKKUsGgt;F [CE] Ekgnig [AB] Rtg; P . 1 > bgajfa [ED] Rsbnwg [AB] .
2 > RsaybBaak;fa ABED CactuekaNBaysm)aT .
3 > KNna DE ebI CD= 5 cm ; OP=2cm . 150 . eKeGayctuekaNe):ag ABCD EdlGgt;RTUg [AC] kat; [BD] Rtg; O . bnat;Rsbnwg (BC) EdlKUsecjBI A kat; (BD) Rtg; E . bnat;Rsbnwg (AD) EdlKUsecjBI B kat; (AC) Rtg; F . bgajfa (EF) Rsb nig (BC) .
151 . eKeGayrgVg; nig manpit nig man kaM nig Edl . rgVg;TaMgBIrb:HKaRtg; A . eKKUsbnat;b:HrYmkgnigbnat;rYmeRkA Edlb:HrgVg; Rtg; B nigb:HrgVg; Rtg; C . bnat;b:HTaMgBIrkat;KaRtg; M .
1 > bgajfa MA=MB=MC nig RtIekaN ABC EkgRtg; A . 2 > bnat; (BA) nig (CA) kat;rgVg; nigrgVg; Rtg; D nig E .
bgajfa [BE] CaGgt;pitnrgVg; ehIy [CD] CaGgt;pitnrgVg; .
3 > bgajfa .
4 > RbdUcRtIekaN BCD nig RtIekaN BCE rYcTajfa
152 . eKeGayrgVg; kaM R ehIyGgt;pitBIrEkgKa [MN] nig [KL] . A CAcMnucmYyenAelIrgVg;
enH. Ggt;F [MA] kat; [KL] Rtg; B .
1 > RsaybMPWfaplKuN MA .MB=MO.MN . 2 > eRbobeFob nig rYcKNna ebI BO=BA .
3 >KNnaRkLap MOB nigMAN kalNa BO=BA .
153 . eKeGayrgVg;pit O kaM R Ggt;pit [AB]. tamcMnuc P mYyenAelIbnayn [AB] KUsbnat;b:H
rgVg;Rtg; T ehIybnat; (PT) kat;bnat;EdlEkgnwg (AB) Rtg; A Rtg;cMnuc D .
1 >bMPWfa RtIekaN OPT nig RtIekaN ADP dUcKa rYcTajykpleFobRCugRtUvKa .
2 > eKeGay KNna PO ; AD ; PD .
3 >KUs [OM] Rsbnwg (AD) . KNna MT nig DM .
4 > RsaybBaak;fa OM = MD .
5 > KNnaRkLapnctuekaN AOMD nig RkLap RtIekaN ODM .
154 . eKeGaykaer ABCD mYy Edl P sitenAelI [BC]. bnat;(AP)kat;(CD)Rtg; Q ehybnat; mYyEkgnwgbnat (AP) Rtg; A kat; (CD) nig (BC) erogKaRtg; S nig R .
1 >bgajfaRtIekaN ASP nig RtIekaN AQR Ca RtIekaNEkgsm)aT /
2 > bnat (PS) Ekg nig (RQ) Rtg; H ehIy N nig M CacMnuckNalerogn [RQ] nig [PS] .
bgajfa AMHN CactuekaNEkg .
3 > bgajfa cMnuc M ; B; N nig D rt;Rtg;Ka .
4 > bgajfa rYcbBaak;fa nig CamMubEnmKa . 5 >snt; nig AB=8cm . KNna BS nigRkLapctuekaNEkg AMHN . 155 .eKeGayrgVg;pit OkaM RGgt;pit [AB]Edl AB= 5cmeKKUsGgt;F [AC]EdlAC = 3 cm . 1 > R)ab;eQaHRtIekaN ABC rYc KNna BC . 2 > KNna nig .
3 >eKKUsemdan[AM]nABCEdlbnayrbs;vakat;rgVg;Rtg;D.bgajfa
156 . eKeGayctuekaNBaayEkg ABCD Ekg Rtg; A nig D ehIy Ggt;RTUg [BD] Ekg nwgRCugeRTt [BC] nig .
1 >KNna .
2 > RsaybMPWfa .
3 > yk KNna CD ; BD ; AB ;AD CaGnuKmn_n a . 157 . ABC CaRtIekaNEkgRtg; AehIy[AH] CakMBs; . DCacMnucmYYyenAelI [AC]. bnat;KUsecj
BI C Ekgnwg (BD) Rtg; E . bnat; (BA) nig (CE) CYbKaRtg; F .
k > eRbobeFobRtIekaN ABD nig ECD .
x > eK]bmafa cUrKNna AC ; AH nig CD .
K > R)ab;RbePTRtIekaN ACF .
158 . eKeGayrgVg;pit OkaM RGgt;pit [BC]Edl BC= 10cm nigGgt; F [AB] . eKKUsbnat;b:H
rgVg; (O) Rtg; C Edlkat; bnay (BA) Rtg; cMnuc D .
1 > R)ab;RbePTRtIekaN ACD .
2 > RbdUc ABC nig ACD rYcTajbgajfa .
3 > ebI cUrKNna AC ; AB ; AD nig CD .
159 . eKeGayknHrgVg;pitmanGgt;pit [BC]Edl BC= 2R nigcMnuc AelIF BCeday.
[AH] CakMBs;nRtIekaN ABC . 1 > KNna AB ; AC nig AH CaGnuKmn_n R .
2 > eKsg;rgVg;manpit A mankaM [AH] . tam B nig C eKKUsbnat; (BD) nig (CE) b:HrgVg; (A) Rtg; D nig E .
k > bgajfa (BC) Cabnat;b:HrgVg; (A) Rtg; H .
x > RbdUcRtIekaN DAB nig RtIekaN ACE .
K > TajbBaak; fa . 160 .[AH] ; [BK]; [CL] CakMBs; nRtIekaN ABC.Rsayfa . 161 . eKeGayrgVg;manpit nig rgVg;TaMgBIrb:HKaxageRkARtg; A . eKKUsbnat;b:HrYmkg
nigbnat;rYmeRkA Edlb:HrgVg; Rtg; B nigb:HrgVg; Rtg; C . bnat;b:HTaMgBIrkat;KaRtg; M .
1 > bgajfa MA=MB=MC nig RtIekaN ABC EkgRtg; A .
2 > bnat; (BA) nig (CA) kat;rgVg; nigrgVg; Rtg; D nig E .
bgajfa [BE] CaGgt;pitnrgVg; ehIy [CD] CaGgt;pitnrgVg; .
3 > RbdUcRtIekaN BCD nig RtIekaN BCE rYcTajfa BC CamFmsmamaRtn BE nig CD .
ehIyrkRbEvg BC ebIkaM OA=4,5m ;
162 . eKeGayrgVg; kaM R ehIyGgt;pitBIrEkgKa [AB] nig [CD] . Ggt;FmYyKUsecjBI A kat; [CD] Rtg; P nigrgVg;Rtg; M .
1 > RsaybMPWfactuekaN OPBM carwkkgrgVg;EdlRtUvbBaak;pit I rbs;va . 2 > eRbobeFob RtIekaN ABM nig RtIekaN APO rYcKNna ebI BO=BA .
3 >KNnaRkLap MOB nigMAN kalNa BO=BA .
163 . tamrUbxagsaMeKeGay [AD) CaknHbnat;BuHmMu A E nig (BE)//(AD) . A k > bgajfa .
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