10.5 Segment Lengths in Circles

10.5 Segment Lengths in Circles - 10.5 Segment Lengths in...

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Unformatted text preview: 10.5 Segment Lengths in Circles Circles p. 629 Thm 10.15 Thm If 2 chords intersect in the interior of a If circle, then circle, B A C D AC * CD = BC * CE F E Ex: Solve for x. Ex 12 * 9 = 18 * x 108 = 18x 6=x 12 18 x 9 Definitions Definitions Tangent segment – a piece of a tangent with one endpt. at the pt. of tangency. SP Secant segment – a piece of a Secant secant containing a chord, with one endpt. in the exterior of the circle & the other on the circle. RP other External secant segment – the piece of a secant seg. that is outside the circle. PQ outside S R Q P Thm 10.16 Thm If 2 secant segs. share the same endpt. If outside the circle, then outside C D E A AB * AC = AE * AD Exterior parts B Whole secant seg. Whole Ex: Solve for x. Ex 11 * 21 = 12 (12 + x) 231 = 144 + 12x 87 = 12x 7.25 = x 10 11 x 12 Thm 10.17 Thm If a secant seg. & a tangent seg. share an If endpt. outside of a circle, then endpt. A B (AB)2 = AC * AD C D Tangent Ext. secant seg. Whole secant seg Ex: solve for x. Ex 302 = x (x + 24) 900 = x2 + 24x x2 +24x – 900 = 0 +24x How do you solve for x? Use the quadratic formula!! − b ± b 2 − 4ac − 24 ± 24 2 − 4(1) ( − 900 ) x= x= 2(1) 2a a = 1 b = 24 c = -900 24 30 x − 24 + 64.62 x= 2 − 24 − 64.62 x= 2 x = 20.31 x = -44.31 Assignment Assignment ...
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