CHORD RULE #1
*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*
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
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
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
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
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
CHORD RULE #2
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
Ex. 5: In A, PR = 2x + 5 and QR = 3x –27. Find x. 2x + 5 = 3x – 27 -2x -2x 5 = x - 27 +27 +27 A x = __ Q 32 P
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