Congruent Chords Lesson 10.2.

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Presentation transcript:

Congruent Chords Lesson 10.2

If two chords are the same distance from the center of a circle, what can we conclude? Theorem 77: If two chords of a circle are equidistant from the center, then they are congruent.

Theorem 78: If two chords of a circle are congruent, then they are equidistant from the center of the circle.

Given: Circle O, AB  CD, OP = 12x – 5, OQ = 4x + 19 Find: OP Since AB  CD, OP = OQ 12x – 5 = 4x + 19 x = 3 Thus, OP = 12(3) – 5 = 31

Given An isosceles Δ has two  sides. If 2 chords of a circle are , then they are equidistant from the center. A Δ with two  sides is isosceles. Circle P, PQ  AB, PR  CB ΔABC is isosceles, with base AC. AB  BC PQ  PR ΔPQR is isosceles