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Date:. Sec 10-2 Concept: Arcs and Chords Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g. DE. DBE. BD. Vocabulary:. Minor Arc ________ Major Arc _______ Central Angle _______ Semicircle __________. <DPE. Find Each Arc: CD _________

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### Date:

Sec 10-2

Concept: Arcs and Chords

Objective: Given properties of arcs of a circle, solve for missing angles as measured by a s.g.

DBE

BD

Vocabulary:

• Minor Arc ________

• Major Arc _______

• Central Angle _______

• Semicircle __________

<DPE

Measure of Minor Arc = Measure of Central Angle

148

328

180

Measure of Minor Arc = Measure of Central Angle

142

218

118

118

AB  BC IFF AB BC

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

3x

mDC = x+20 =10+20

=30

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

• 3x= x+20

• -x -x

• 2x=20

• 2

• X=10

IF PG DF,

Then DE  EF and

DG  GF

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

AB  CD IFF EG  EF

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

6

6

6

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

Since CG is  AB, AG  GB

Also, CF is  DE, so, DF  FE

Also, if AB = DE, then GC=CF

Use pyth. Thm to find x, that will also be CG.

X2+62 = 72

X2+36 = 49

-36 -36

X2= 13

X=3.6

### Date:

Sec 10-3

Concept: Inscribed Angles

Objective: Given an inscribed angle, find arc measures as measured by s.g.

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

Intercepted Arc

Inscribed Angle

x

Example: Find the measure of the angle

Measure of Inscribed Angle = ½ the intercepted Arc

X = ½ the arc

X=1/2(80)

X=40

60

Find the measure of the Arc

Measure of Inscribed Angle = ½ the intercepted Arc

60 = ½ x

½ ½

X=120

70

B

A

C

C

A

D

mAC = _______

Example: Find the measure of each arc or angle

180

140

72

C

A

Find the measure of <BCA

36

m<BCA = ______

44

A

C

D

Find m<C

M<C = 44

88