a b c d ab = cd

9 2 6 x X = x X = x X = 1 Example 1:

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

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

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

Ex. 1 If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc. y24 x 60  x = 24 y = 30

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

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

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

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

Ex. 5: In  A, PR = 2x + 5 and QR = 3x –27. Find x. P R Q A x = 32

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