1. Properties of Chords

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
120 60
x = ? D
x = 60

3. 2x
x + 40
2x = x + 40
x = 40

4. 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

5. 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

6. 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

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

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

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

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

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

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

13. 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