1. CHORD RULE #1

2. *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 is perpendicular to AB C P A R D B
*YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*

3. AC is the _____________
What can you tell me about segment AC if you know it is the perpendicular bisector of segment DB? D
AC is the _____________
diameter A C B

4. Ex. 1 If a diameter of a circle is __________ to a chord, then the diameter ___________ the chord and its arc.
perpendicular
bisects
Find x: 24
x = _____ 24 x

5. Example 2
EX 2: IN P, if PM  AT, PT = 10, and PM = 8, find MT and AT. P A
*HINT: Label your segment lengths.
*HINT: Use the Pythagorean theorem. M
MT = __ 6 T
AT = __ 12

6. 8 RZ = _____ Example 3 In R, XY = 30, RX = 17, and RZ  XY. Find RZ.
*HINT: Find the measure of XZ first. X 8
RZ = _____ R Z Y

7. x =_____ 4 Example 4: IN Q, KL  LZ. IF CK = 2X + 8 and
CZ = 4x, find x.
*HINT: How is CK related to CZ? Q
x =_____ 4 C Z K L

8. CHORD RULE #2

9. 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
*IFF: If and Only If

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

11. 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
-3x + 56 = 4x K E
x = __ 8 R S Y