Apply Properties of Chords

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Presentation transcript:

10.3.1 Apply Properties of Chords Chapter 10: Circles 10.3.1 Apply Properties of Chords

Arcs and Chords For any circle (or congruent circles), two arcs are congruent iff their corresponding chords are congruent Congruent Chord Congruent Arc (CCCA) A AD  BE iff C B AD  BE D E

Chord Diameter relationship A chord is a perpendicular bisector of another chord iff the perpendicular chord is a diameter Chord Diameter Perpendicular Bisector Theorem (CDP) The diameter bisects the arc formed by the chord BD  DE A iff BF  FE B C and F BE ┴ (Diameter) D E

Chord Distance Theorem Two chords are congruent iff they are equidistant from the center of the circle (or congruent circles) A GC  FC iff C AD  BE G B iff F D AD  BE (how do we know?) E

Find the value of x and y for each circle Find the values of x and y so that AD = BE AD = 180⁰ BF = 13x – 2y FE = 20 BD = 20⁰ DE = 8.5x +y A A (x – y)⁰ C G B C 3y - 5 B F x F D D 25⁰ E E +

Homework p. 667 1, 2, 3 – 35odd, 37