Properties of Chords

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 120 60 x = ? D x = 60

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

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

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

Two chords are congruent if and only if they are equidistant from the center. F G if and only if KL=KM k M J L F H G

LC = 10x and MC = 3x+2. Find the value of x 10𝑥=3𝑥+2 7𝑥=2 𝑥=3.5

Find the radius If AE = 24 and DO=5 𝑎 2 + 𝑏 2 = 𝑐 2 24 5 2 + 12 2 = 𝑐 2 169= 𝐶 2 169 = 𝐶 2 5 13=𝐶 12

EX 2: In P, if PM  AT, PT = 10, and PM = 8, find AT.

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.

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