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10.5 Segment Lengths in Circles

10.5 Segment Lengths in Circles. p. 629. Thm 10.15. If 2 chords intersect in the interior of a circle, then AC * CD = BC * CE. B. A. C. D. F. E. Ex : Solve for x. 12 * 9 = 18 * x 108 = 18x 6 = x. x 18. 12 9. R. Definitions. S.

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10.5 Segment Lengths in Circles

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  1. 10.5 Segment Lengths in Circles p. 629

  2. Thm 10.15 If 2 chords intersect in the interior of a circle, then AC * CD = BC * CE B A C D F E

  3. Ex: Solve for x. 12 * 9 = 18 * x 108 = 18x 6 = x x 18 12 9

  4. R Definitions S Tangent segment – a piece of a tangent with one endpt. at the pt. of tangency. Secant segment – a piece of a secant containing a chord, with one endpt. in the exterior of the circle & the other on the circle. External secant segment – the piece of a secant seg. that is outside the circle. SP Q RP P PQ

  5. Thm 10.16 If 2 secant segs. share the same endpt. outside the circle, then AB * AC = AE * AD Exterior parts Whole secant seg. C D B E A

  6. Ex: Solve for x. 11 * 21 = 12 (12 + x) 231 = 144 + 12x 87 = 12x 7.25 = x 10 11 x 12

  7. Thm 10.17 If a secant seg. & a tangent seg. share an endpt. outside of a circle, then (AB)2 = AC * AD Tangent Ext. secant seg. Whole secant seg B A C D

  8. Ex: solve for x. 24 302 = x (x + 24) 900 = x2 + 24x x2 +24x – 900 = 0 How do you solve for x? Use the quadratic formula!! x = 20.31 x = -44.31 30 x a = 1 b = 24 c = -900

  9. Assignment

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