10.3 - ARCS AND CHORDS

Objective: Determine missing parts of a circle using

properties of chords and arcs

ARC Minor: connects an angle under 180˚ Major: connects an angle over 180˚

CHORD A segment whose endpoints are points on a

circle.

Butterfly Theorem:Two minor arcs are congruent if and only if their corresponding chords are congruent.

ABCD if and only if ABCD

A

B

C

D

Find mCD.

4x°

E

D

C

x + 78°

B

Vitruvian Theorem:If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

DEEF, DGGF

F

G

E

D

OIf OG is a diameter of circle O, then

Using the Vitruvian Theorem

Tug-of-War Theorem:Two chords are congruent if and only if they are equidistant from the center.

A

F

C

BABCD if and only if EFEG

D

G

What happens if the segment is also perpendicular?

Find CG.

E

D

C

B

G

A

F

12

12

8

Find CE.

In Circle R, LM = NO, LM = 6, TR = 4 mLM = 80.

1.) Find mNQ. 2.) Find TO. 3.) Challenge: Find RP.

AD = 40 and CD = 25. Find CG.

ED

C

B

G

A

F

Find the length of a chord of a circle with radius 8 that is a distance of 5 from the center.

AB = 12, DE =12, and CE = 7. Find CG.

E

D

C

B

G

A

F

Homework:p. 719-720 #12,15-19, 21-23,

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