10.6 Find Segment Lengths in Circles discovery time! complete the 10.6 Clock activity sheet

Theorem: If two ________ intersect in a circle, then the _________ of the measures of the ___________ of the chords are ___________. Therefore, ______________ chords products equal segments ad = bc

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

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

Examples (x+3)3 = (7+4)4 9x = 18 3x + 9 = 44 x = 2 x = 11.7 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 9x = 18 3x + 9 = 44 x = 2 x = 11.7

Examples (9+4)4 = x² (6+x+3)6 = 12² X = 7.2 54+6x = 144 X = 15 Find the value of x to the nearest tenth. Assume that the segments that appear to be tangent are tangent: 3. 4. (9+4)4 = x² (6+x+3)6 = 12² X = 7.2 (9+x)6 = 144 54+6x = 144 X = 15 2y = 15*3 y = 22.5

Homework ws

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