1. In , BD is a diameter and

mAOD = 55. Find mCOB.

2. Find mDOC.

3. Find mAOB.

4. Refer to . Find .

5. Find .

• inscribed

• circumscribed

• Recognize and use relationships between arcs and chords.

• Recognize and use relationships between chords and diameters.

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Prove Theorem 10.2

PROOF Write a two-column proof.

Prove:

Given:

is a semicircle.

Prove Theorem 10.2

Proof:Statements Reasons

5. Def. of arc measure5.

4. Def. of arcs4.

2. Def. of semicircle2.

3. In a circle, if 2 chords are , corr. minor arcs are .

3.

Answer:

1. 1. Givenis a semicircle.

Prove Theorem 10.2

Answer:

6. 6. Arc AdditionPostulate

7. 7. Substitution

8. 8. Subtraction Property and simplify

9. 9. Division Property

11. 11. Substitution

Statements Reasons

10. 10. Def. of arc measure

PROOF Choose the best reason to complete the following proof.

Prove:

Given:

Proof:Statements Reasons

1.

2.

3.

4.

1. Given

2. In a circle, 2 minor arcs are , chords are .

3. ______

4. In a circle, 2 chords are , minor arcs are .

A. A

B. B

C. C

D. D

A. Segment Addition Postulate

B. Definition of

C. Definition of Chord

D. Transitive Property

A regular hexagon is drawn in a circle as part of a logo for an advertisement. If opposite vertices are connected by line segments, what is the measure of angle P in degrees?

Since connecting the opposite vertices of a regular hexagon divides the hexagon into six congruent triangles, each central angle will be congruent. The measure of each angle is 360 ÷ 6 or 60.

Answer: 60

1. A

2. B

3. C

ADVERTISING A logo for an advertising campaign is

a pentagon that has five congruent central angles.

Determine whether

A. yes

B. no

C. cannot be determined

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Radius Perpendicular to a Chord

Radius Perpendicular to a Chord

Since radius is perpendicular to chord

Arc addition postulate

Substitution

Substitution

Subtract 53 from each side.

Radius Perpendicular to a Chord

Radius Perpendicular to a Chord

A radius perpendicular to a chord bisects it.

Definition of segment bisector

Draw radius Δ

Radius Perpendicular to a Chord

Use the Pythagorean Theorem to find WJ.

Pythagorean Theorem

Simplify.

Subtract 64 from each side.

Take the square root of each side.

JK = 8, WK = 10

Radius Perpendicular to a Chord

Answer: 4

Segment Addition Postulate

Subtract 6 from each side.

WJ = 6, WL = 10

1. A

2. B

3. C

4. D

A. 35

B. 70

C. 105

D. 145

1. A

2. B

3. C

4. D

A. 15

B. 5

C. 10

D. 25

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Chords Equidistant from Center

Chords Equidistant from Center

are equidistant from P, so .

Answer: PR = 9 and RH = 12

Chords Equidistant from Center

Draw to form a right triangle. Use the Pythagorean Theorem.

Pythagorean Theorem

Simplify.

Subtract 144 from each side.

Take the square root of each side.

A. A

B. B

C. C

D. D

A. 12

B. 36

C. 72

D. 32

A. A

B. B

C. C

D. D

A. 12

B. 36

C. 72

D. 32