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10.3 - ARCS AND CHORDS
Objective: Determine missing parts of a circle using
properties of chords and arcs
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ARC Minor: connects an angle under 180˚ Major: connects an angle over 180˚
CHORD A segment whose endpoints are points on a
circle.
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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
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Find mCD.
4x°
E
D
C
x + 78°
B
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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
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Using the Vitruvian Theorem
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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?
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Find CG.
E
D
C
B
G
A
F
12
12
8
Find CE.
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In Circle R, LM = NO, LM = 6, TR = 4 mLM = 80.
1.) Find mNQ. 2.) Find TO. 3.) Challenge: Find RP.
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AD = 40 and CD = 25. Find CG.
ED
C
B
G
A
F
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Find the length of a chord of a circle with radius 8 that is a distance of 5 from the center.
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AB = 12, DE =12, and CE = 7. Find CG.
E
D
C
B
G
A
F
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Homework:p. 719-720 #12,15-19, 21-23,
38