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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 A If the radius is 8 A B 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=7 QA=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 C B XY

BX + XA=BA 6+XA= 11 XA=5

Find the exact circumference of circle A. (Hint: use Pythagorean theorem.) A 8 15

64+225=c squared 289=C C= 17 Circumference = Pi x diameter Circumference of circle A = 53.41

Find Angle CAE( Hint: Angles CAE and EAB are linear pairs) A CB D E F 225x 4x 3x

25x+4x+3x=180 32x=180 X= (5.625) =

Find the measure of arc EF A B 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 24pi 120/360=AC/24pi 120/360(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 the measure of angle BAC. A.144 degreesB. 72 degreesC. 150 degrees144 degreesB. 72 degreesC. 150 degrees D. 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 A 40 degrees BC DF E

DE=40 CDE= 130 FCE= 220

A regular octagon is inscribed in a circle as part of a stained glass art piece. 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 DE FG 10

(CG)^2+(GA)^2=(CA)^2 (CG)^2+10^2=30^2 (CG)^2=100=900 (CG)^2=800 CG= CG=1/2(GA), so GA=2( ) or CF is congruent to DB, so DG also equals DF=1/2 of DG so DF=

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

6^2+x^2=10^2 36+x^2=100 X^2=64 X=8 BD=8 BC=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 of CE, CF, BG, and BD. A B C DE FG 6

6^2+x^2=10^2 36+x^2=100 X^2=64 X=8 CE=8 CF=16 BD=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 angle2 X=2x-20 X=20Angles 1 and 2=20

Triangles BDE and BEC are inscribed in circle A with arc BD Congruent 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=180 X=6 Angle 1=64, angle 2=26

Measure of angle D=1/3x+5 Measure 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=51 Angle 2=90 Angle 3=39

Quadrilateral BCDE is inscribed in a circle. Find the measure of angles D and E. A B C D E

Angle D=145 Angle 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.

Sometimes Always Sometimes

A Chord that passes through the center of a circle.

Diameter

The distance around a circle.

Circumference

An arc that measures less than 180 degrees. An arc that measures greater than 180 degrees. An arc that measures 180 degrees

Minor Arc Major Arc Semicircle

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 DE Prove: GF is congruent to ED (Theorem 10.2) B F D E G

1.Circle B, arc GF s congruent to arc DE-GivenCircle B, arc GF s congruent to arc DE-Given 2.Angle GBF is congruent to angle EBD- if arcs are congruent, theirAngle GBF is congruent to angle EBD- if arcs are congruent, their Corresponding central angles are congruent. 3. GB is congruent to FB is congruent to BE is congruent to DB- all Radii of a circle are congruent 4. Triangle GBF is congruent to Triangle EBD- SAS 5. GF is congruent to ED- CPCTC