Geometry 9 4 Arcs and Chords Theorem In

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 130 110 Y 22 15 U V 1. Z 12 P X 10 Q W 8 110 140 R 2. 130 115

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

Exercises K A 4 B H G 3 Q 6 D C Q Q 12 J F M E 200˚ 3. 4. 5 12 5. 80

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 8 B Y O 8 D 9. 12 DC = ____ X C 6 6 S √ 2 6 12 A Q F K E H O R 6√ 2 M 12√ 2 G 9 18 OO N T P 3 √ 9 11. 10. 6√ 2 18√ 3

Exercise (like on your homework) 12. Sketch a circle O with radius length 17 and a chord that has a length 30. How far is the chord from O? A 17 15 30 8 17 ●O Pythag. Triple 8 -15 -17 B The chord is 8 units from circle O.

Exercise (like on your homework) 13. Sketch a circle R with radius length 5√ 3 and a chord that is 5 units from R. Find XY. 5√ 3 R Y 5√ 3 ● 5 x Pythag. Thm: 5²+x²= (5√ 3)² x² + 25 = 75 x² = 50 x = 5√ 2 2 ● 5√ 2 = 10√ 2 X Chord XY is 10√ 2 units long.

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