1. 52.5° 4
Brain Buster
32° 2 3
105°
36.5° 1
105°
16°

2. In the same circle, or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent. B C
AB  CD IFF AB  DC A D

3. 60
120
120 x
x = 60

4. 2x
x + 40
2x = x + 40
x = 40

5. *YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*
If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
IF: AD  BD and AR  BR
THEN: CD  AB C P A R D B
*YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*

6. What can you tell me about segment AC if you know it is the perpendicular bisectors of segments DB?
It’s the DIAMETER!!! A C B

7. Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.
x = 24 24 y
60
y = 30 x

8. Example 2
EX 2: IN P, if PM  AT, PT = 10, and PM = 8, find AT. A P
MT = 6 M
AT = 12 T

9. RZ = 8 Example 3 In R, XY = 30, RX = 17, and RZ  XY. Find RZ. X R Z

10. x = 1.5 Example 4 IN Q, KL  LZ. IF CK = 2X + 3 and CZ = 4x, find x.

11. You try… 10.2 Practice B 19 – 27

12. In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. B
AD  BC
IFF
LP  PM A M P L C D

13. Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x.

14. Ex. 6: IN K, K is the midpoint of RE
Ex. 6: IN K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find x. U T K E R S
x = 8 Y

15. You try… 10.2 Practice B
28 – 29

16. Two chords intersect
INSIDE the circle
Type 1: a
ab = cd d c b

17. Example 1: 9 12 6 3 x x 2 2
X = 3
X = 8 x 3 6 2
X = 1

18. Example 2: Find x
2x  3x = 12  8 8 12 2x 3x
6x2 = 96
x2 = 16
x = 4