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10.2 10.4 Vocabulary

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10.310.1

Circle A has diameters BD and CE.If BD =12 and CE=12, find BA.

A

B

C

E

D

BA=6

Find the Circumference of Circle AIf the radius is 8

AB

C

D

E

Circumference = 50.27

Circle A has diameters BD and CE. If BD and CE both = 14,Find the Radius of BA and CA. Once you solve for CA and BA, solve For QA.

A

B

C

D

E

Q

BA and CA=7QA=7

The diameter for circle B is 12 inches, the diameter of circle A is 22 Inches, and the diameter of circle C is 14 inches. Find XA.

A CB X Y

BX + XA=BA6+XA= 11

XA=5

Find the exact circumference of circle A. (Hint: use Pythagorean theorem.)

A8

15

64+225=c squared289=CC= 17

Circumference = Pi x diameterCircumference of circle A = 53.41

Find Angle CAE( Hint: Angles CAE and EAB are linear pairs)

AC B

D

E

F225x

4x

3x

25x+4x+3x=18032x=180X= 5.625

25(5.625) =140.625

Find the measure of arc EF

AB

C

E

D

F

45 degrees

EF= 45 degrees

AB=12 and angle BAC=120 degrees, find the length of arc BC.

A

B

C

120 degrees

C=2(pi)(12) or 24pi120/360=AC/24pi120/360(24pi)=AC

25.13=AC

In circle A, BA is the radius and BC is a minor arc.If BA=5 inches and the length of BC is 4Pi inches, what is themeasure of angle BAC.A.144 degreesB. 72 degrees C. 150 degreesD. 120 degrees.

A

B

C

A. 144 degrees

In circle A, angle BAF=40 degrees and CA bisects AD. Find arc BE, arc CDE, and arc FCE

A40 degrees

B C

DF

E

DE=40 CDE= 130 FCE= 220

A regular octagon is inscribed in a circle as part of a stained glass artpiece. If opposite vertices are connected by a line segment, what is

The measure of angle BAC?

A

B

C

Angle BAC = 135

Chords CE and BD are equidistant from the center.If the radius of circle A is 30, find CE and FD

A

B C

D E

F G10 10

(CG)^2+(GA)^2=(CA)^2(CG)^2+10^2=30^2

(CG)^2=100=900(CG)^2=800CG=28.2843

CG=1/2(GA), so GA=2(28.2843) or 56.5685CF is congruent to DB, so DG also equals 56.5685.

DF=1/2 of DG so DF=28.2843

The radius of Circle A= 10, AD=6Find BD and BC.

A

B

C

D6

6^2+x^2=10^236+x^2=100

X^2=64X=8

BD=8BC=16

Determine the measure for the arc of the circle circumscribed about the traffic sign.

A

A

B

C

D

Measure of arc AB= arc BC= arc CD= arc DA=90

In circle A, BG is congruent to CF and AC=10 Find the measures ofCE, CF, BG, and BD.

A

B C

D E

FG

6

6^2+x^2=10^236+x^2=100

X^2=64X=8

CE=8CF=16BD=8

BG=16

Find the measure of each numbered angle for the figure above.Measure of angle 1=x, measure of angle 2=2x-20

A

1 2

Measure of angle 1=measure of angle2X=2x-20

X=20Angles 1 and 2=20

Triangles BDE and BEC are inscribed in circle A with arc BDCongruent to arc DE. Find the measure of angle 1 and angle 2 if the

Measure of angle 1= 12x-8 and measure of angle 2= 3x+8

A

B

C

D

E

1

2

Measure of angle 1+measure of angle 2+ measure of angle BCE=180X=6

Angle 1=64, angle 2=26

Measure of angle D=1/3x+5Measure of angle B= 1/2x

Find the measure of each numbered angle for the figure above

A

B

C D

1

2 3

Angle 1=51Angle 2=90Angle 3=39

Quadrilateral BCDE is inscribed in a circle. Find the measure ofangles D and E.

A35

100

B

C

D

E

Angle D=145Angle E=80

Acute Angles are_____ equilateral.Equilateral triangles are _____ isosceles.

Obtuse triangles are _____ Scalene.

Fill in the following statements with sometimes, always or never.Each word can be used more than once.

SometimesAlways

Sometimes

A Chord that passes through the center of a circle.

Diameter

The distance around a circle.

Circumference

An arc that measures less than180 degrees.

An arc that measures greater than180 degrees.

An arc that measures 180 degrees

Minor ArcMajor ArcSemicircle

The measure of an arc formed by two adjacent arcs in the sum of the measures of two arcs.

Postulate 10.1

In a circle or in congruent circles,Two chords are congruent if and only

If they are equidistant from the center.

Theorem 10.4

PLACE YOUR WAGER!

Given: Circle B, arc GF is congruent to arc DEProve: GF is congruent to ED

(Theorem 10.2)

B

F

D

E

G

1. Circle B, arc GF s congruent to arc DE-Given2. Angle GBF is congruent to angle EBD- if arcs are congruent, theirCorresponding central angles are congruent.3. GB is congruent to FB is congruent to BE is congruent to DB- all Radii of a circle are congruent4. Triangle GBF is congruent to Triangle EBD- SAS5. GF is congruent to ED- CPCTC