Geometry 9.4 Arcs and Chords

Theorem In the same circle or in congruent circles: congruent arcs have congruent chords congruent chords have congruent arcs ● O

Exercises 110  X Y V U W Z 130  Q P R 

Theorem A diameter that is perpendicular to a chord bisects the chord and its arc. ● O

Exercises Q G H J M K Q A B C Q D E F ˚

Theorem In the same circle or in congruent circles: chords equally distant from the center (or centers) are congruent congruent chords are equally distant from the center (or centers) ● O

Exercises O A Y B D C X DC = ____ 12 H E F K G O M 12√2 6√2 12√2 6√2 N O 9 P Q S R T 18 O 9√3 18√3

Exercise (like on your homework) 12. ● A B The chord is 8 units from circle O. 8 Pythag. Triple O

Exercise (like on your homework) 13. ● 5√3 5 Y X Chord XY is 10√2 units long. Pythag. Thm: 5²+x²= (5√3)² x² + 25 = 75 x² = 50 x = 5√2 2 ● 5√2 = 10√2 5√3 x R

Homework pg. 346 CE #1-5 WE # 1-13