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# Point Y is on a circle and point P lies outside the circle such that PY is tangent to the circle. Point A is on the circle such that segment PA meets the

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Point Y is on a circle and point P lies outside the circle such that PY is tangent to the circle. Point A is on the circle such that segment PA meets the circle again at point B. If PA = 15 and PY = 9, then what is AB?

Guest Mar 20, 2017
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#1
+79654
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We can use the secant-tangent theorem, here....specifically........

PA * PB  = (PY)^2

15* PB  = (9)^2

15 * PB   = 81     divide both sides by 15

PB  = 81 / 15

PB = 27 / 5

So...AB  = PA - PB  =    15 - 27/5    =   45/5 - 27/5   =  18/5

CPhill  Mar 20, 2017
#2
+26357
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Typo in the last line Chris.  15 = 75/5 so:  PB = 75/5 - 27/5 = 48/5

.

Alan  Mar 21, 2017

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