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

120 ○ 12 x x = 12 in. What is the length of the chord labeled “x”?

2x + 10 x x + 10= x + 40 x = 30

A B C D What can you tell 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. y4 x 60  x = 4 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 If and only if 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