1. Geometry
9.4
Arcs and Chords

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

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

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

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

6. 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

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

8. Exercise (like on your homework)
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 17 15 ● O 30 8
Pythag. Triple B
The chord is 8 units from circle O.

9. 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
Pythag. Thm:
5²+x²= (5√3)²
x² + 25 = 75
x² = 50
x = 5√2
2 ● 5√2 = 10√2 R
5√3 Y ● x 5 X
Chord XY is 10√2 units long.

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