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Warm-Ups for Circles

Warm-Ups for Circles. Warm up #2. Warm Up #3. Hint: Draw a picture to represent the situation. CHORD RULE #1. 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.

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Warm-Ups for Circles

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  1. Warm-Ups for Circles

  2. Warm up #2

  3. Warm Up #3 Hint: Draw a picture to represent the situation

  4. CHORD RULE #1

  5. 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 perpendicularto AB C P A R D B *YOU WILL BE USING THE PYTHAGOREAN THM. WITH THESE PROBLEMS sometimes*

  6. 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

  7. 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

  8. 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

  9. 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

  10. 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

  11. CHORD RULE #2

  12. In the same circle or in congruent circles, two chords are CONGRUENT if and only if they are equidistantfrom theCENTER. B AD  BC IFF LP  PM A M P L C D *IFF: If and Only If

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

  14. 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

  15. Homework: Page 201 1-13

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