1. 10.3.1 Apply Properties of Chords
Chapter 10: Circles
Apply Properties of Chords

2. 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

3. 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

4. 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

5. 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 +

6. Homework
p. 667
1, 2, 3 – 35odd, 37