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10.5 Segment Measures

10.5 Segment Measures. Two chords intersect INSIDE the circle. Type 1:. a. ab = cd. d. c. b. Example 1:. 9. 12. 6. 3. x. x. 2. 2. X = 3. X = 8. x. 3. 6. 2. X = 1. 12. 2x. 8. 3x. 2x  3x = 12  8. 6x 2 = 96. x 2 = 16. x = 4. Example 2: Find x.

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10.5 Segment Measures

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  1. 10.5 Segment Measures

  2. Two chords intersect INSIDE the circle Type 1: a ab = cd d c b

  3. Example 1: 9 12 6 3 x x 2 2 X = 3 X = 8 x 3 6 2 X = 1

  4. 12 2x 8 3x 2x  3x = 12  8 6x2 = 96 x2 = 16 x = 4 Example 2: Find x

  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  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 bisectors of segments DB? D It’s the DIAMETER!!! A C B

  7. Ex. 1 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

  8. EX 2: IN P, if PM  AT, PT = 10, and PM = 8, find AT. P A M MT = 6 T AT = 12 Example 2

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

  10. IN Q, KL  LZ. IF CK = 2X + 3 and CZ = 4x, find x. Q x = 1.5 C Z K Example 4 L

  11. B AD  BC IFF LP  PM A M P L C In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. D

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

  13. U T K E R S x = 8 Y Ex. 6: IN K, K is the midpoint of RE. If TY = -3x + 56 and US = 4x, find x.

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