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

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

60 120 120 x x = 60

2x x + 40 2x = x + 40 x = 40

*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*

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

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

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

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

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

You try… 10.2 Practice B 19 – 27

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

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

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

You try… 10.2 Practice B 28 – 29

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

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

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