Date:

Sec 10-2Concept: Arcs and ChordsObjective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g.

Vocabulary:

1. Minor Arc ________

2. Major Arc _______

3. Central Angle _______

4. Semicircle __________

DE

DBE

<DPE

BDP

B

D

E

Measure of Minor Arc = Measure of Central Angle

A

D

B

C

148

Find Each Arc:

a. CD_________

b. CDB ________

c. BCD _________

148

328

180

Measure of Minor Arc = Measure of Central Angle

Find Each Arc:

a. BD_________

b. BED ________

c. BE _________

142

218

118 A

E

B

C

D

100

6082

118

Thm 10-4: In the same or congruent circles, 2 minor arcs are congruent if and only if their corresponding chords are congruent.

P

C

A

B

AB BC IFF AB BC

Example: Find mDC given AD = 3x, DC = x+20

B

D

A C

3x X+203x= x+20

-x -x

2x=20

2 2

X=10

mDC = x+20 =10+20

=30

Thm 10-5: If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc

P

G

FD E

IF PG DF,

Then DE EF and

DG GF

Thm 10-7: In the same or in congruent circles 2 chords are congruent IFF they are equidistant from the center.

E

B

C

D

A

G

F

AB CD IFF EG EF

Example: AB =12, DE =12 , CE = 7, Find CG

66

6

6

C

E

A

B

D

F

G

x

7

12

12

Since CG is AB, AG GB

Also, CF is DE, so, DF FE

Also, if AB = DE, then GC=CFUse pyth. Thm to find x, that will also be CG.

X2+62 = 72

X2+36 = 49

-36 -36

X2= 13

X=3.6

Proof:

Date:

Sec 10-3Concept: Inscribed AnglesObjective: Given an inscribed angle, find arc measures as measured by s.g.

Inscribed Angle:

An angle whose vertex is on a circle and whose sides contain chords of the circle.

Inscribed Angle

Intercepted Arc

Example: Find the measure of the angle

Measure of Inscribed Angle = ½ the intercepted Arc

80

x

X = ½ the arc

X=1/2(80)

X=40

x

60

60 = ½ x

½ ½

X=120

Find the measure of the Arc

Measure of Inscribed Angle = ½ the intercepted Arc

Example: Find the measure of each arc or angle

B

AC

D

mADC = ______180

mAC = _______

70

B

A

C

140

Find the measure of <BCA

m<BCA = ______36

B

AC

72

Find m<C

A

B

C

D

44

88

M<C = 44

Example:

Proof:

Today’s work