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Understanding Congruent Chords in Circles: Properties and Theorems

This lesson explores the properties of congruent chords in a circle, focusing on Theorems 77 and 78. Theorems state that if two chords are equidistant from the center, they are congruent, and vice versa. Through examples and calculations involving Circle O and congruent chords AB and CD, we find the lengths of segments OP and OQ. Understanding these theorems helps in solving various geometric problems involving circles.

patience-kelly
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Understanding Congruent Chords in Circles: Properties and Theorems

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  1. Lesson 10.2 Congruent Chords

  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.

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

  4. 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

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

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