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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
 #1
avatar+88871 
+2

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

 

 

cool cool cool

CPhill  Mar 20, 2017
 #2
avatar+26971 
+1

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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