10 6 Find Segment Lengths in Circles Theorem

10. 6 Find Segment Lengths in Circles

Theorem: If two ____ intersect in a circle, then the _____ chords products of the equal measures of the ______ of the chords are ______. segments ad = bc Therefore, _______

More Theorems: Terms for next two theorems: secant segments: A segment from a point exterior to a circle to a point on the circle and containing a chord of the circle (AC or AD). external secant segments: Part of a secant segment that is exterior to the circle (AB or AE). secant segments are drawn to a circle from an ____ exterior point, If two ______ product the measures of one secant segment and its then the ______of _____ to the product of the equalsecant segment is _____ external measures of the other secant segment and its external secant segment. AE External Secant Segments: ____ and _______ AB AC*AB so that basically… _____ = _______ AD*AE (CB + BA) BA = (DE + EA) EA

More Theorems: tangent segment and a _______ secant segment are drawn to a circle If a ____ square of the measure of the from an ____ external point, then the _______ tangent segment is ______ equal to the _______ product of the measures of the _______ secant segment and its external secant segment. XZ*XY XW 2 Basically… ____ = ______ (ZY + YX)YX

Examples Find the value of x to the nearest tenth. Assume that the segments that appear to be tangent are tangent: 1. 2. (x+3)3 = (7+4)4 3 x + 9 = 44 x = 11. 7 9 x = 18 x=2

Examples Find the value of x to the nearest tenth. Assume that the segments that appear to be tangent are tangent: 3. (9+4)4 = x² X = 7. 2 4. (6+x+3)6 = 12² (9+x)6 = 144 54+6 x = 144 X = 15 2 y = 15*3 y = 22. 5

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