Geometry - 1

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Question – 1

Night Classe

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Question – 2

Night Classe

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How many triangles with perimeter = 14 can be formed such that it sides are integer?

(1) 6 (2) 4

(3) 3 (4) 7

Question – 3

Night Classe

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Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?

(1) 5 (2) 21 (3) 10

(4) 15 (5) 14

CAT 2008

Question – 4

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Question – 5

How many triangles with altitudes 6, 8 and x can be formed such that x is an integer?

(1) 20 (2) 9

(3) 11 (4) 19

Night Classe

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In quadrilateral PQRS, PQ = 5 units, QR = 17 units, RS = 5 units, and PS = 9 units. The length of the diagonal QS can be:

XAT 2014

(1) > 10 and < 12

(2) > 12 and < 14

(3) > 14 and < 16

(4) > 16 and < 18

(5) Cannot be determined

Question – 6

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Question – 7

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Question – 8

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Question – 9

A, B and C of a triangle are in arithmetic progression. Which of the following is definitely true? (a, b, c are the lengths of the sides opposite to A, B and C respectively)

(1) a2 + b2 = c2 + ab

(2) b2 + c2 = a2 + bc

(3) c2 + a2 = b2 + ac

(4) a2 + b2 = c2

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Question – 11

In ABC right angled at B, P and Q are mid points of sides AB and BC respectively. Which of the following is true?

(1) AQ2 + CP2 = AC2

(2) AQ2 + CP2 = AC2

(3) AQ2 + CP2 = AC2

(4) AQ2 + CP2 = AC2

(5) None of these

76

5465

Night Classe

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Question – 12

In the figure given below, and BC = 20 cm. AD is drawn

perpendicular on BC such that it meets BC produced at D. Find the length of AD.

(1) (2) (3)

(4) (5)

ABC = 45°, ACB =120°

3 1sin 152 2

120° 20

45°

A

B

C

10 3 3 10 3 – 3 5 3+ 3

5 3 – 3 10 3 + 2

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Similar triangles

Night Classe

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In the adjoining figure QPR = SQR. If QR = 12, QS = 7 and SR = 9, find the ratio of the perimeter of PQR to that of SQR.

(1) (2) (3)

(4) (5)

Question – 13

P

Q R

S

7

12

9

57

43

139

1914

47

Similar triangles

Night Classe

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ABC is a right-angled triangle, right angled at B. If AD = 8 cm, DC = 2 cm and , then find the length of BD.

(1) 4 cm (2) 4.5 cm (3) 5 cm

(4) 5.5 cm (5) Cannot be determined

Question – 14

A

B C

D

8

2

BD AC

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Question – 15

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Question – 16

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In ABC, points P, Q and R are on sides AB, BC and CA respectively such that AP : PB = 2 : 3, BQ : QC = 5 : 4, CR : RA = 3 : 4. If the area of PQR = 78 sq. cm, then find the area of ABC.

(1) 315 sq. cm (2) 241 sq. cm (3) 280 sq. cm

(4) 340 sq. cm (5) 380 sq. cm

Question – 17

A

B C

P

Q

R

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In the adjoining figure, if RB, SC and TD are perpendiculars to BD, then is equal to

(1) (2) (3)

(4) (5)

Question – 18

R

BC D

ST

x

p q

yz

pq

pp q

qp

qp q

pqp q

xy

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Question – 19

In right angled triangle ABC right angled at B, AB = 1 unit, BC = 2 units. D is a point on AC such that BD = AB and E is the foot of the perpendicular from D on BC. The area of triangle BDE as a fraction of the area of triangle ABC is

(1) (2)

(3) (4)

925

35

625

725

Night Classe

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Properties of four centres in a triangle

Area of ABD = area of ADC

Median:

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Properties of four centres in a triangle

Angle Bisector:

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Properties of four centres in a triangle

Angle Bisector:

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Properties of four centres in a triangle

Perpendicular Bisector:

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Properties of four centres in a triangle

Altitude:

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Properties of four centres in a triangle

Night Classe

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In ABC, ‘O’ is the point of intersection of the altitudes and I is the point of intersection of the angle bisectors. If BOC = 130°, then find the measure of BIC.

(1) 125°

(2) 120°

(3) 105°

(4) 95°

(5) 115°

Question – 20

Properties of four centres in a triangle

Night Classe

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In ABC, D and E are points on side AC such that AD : DE : EC is 2 : 1 : 1. BD and BE are joined. Point F and G are on BD and BE respectively such that BF : FD = 1 : 2 and BG : GE = 2 : 1. Find the ratio of the area of (AFG BFG) to the area of the ABC.

(1) 2 : 5 (2) 3 : 10 (3) 1 : 3

(4) 1 : 4 (5) 2 : 7

Question – 29

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