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A, B, and T are three points lying on a circle.  If PT is a tangent line of the circle and AB = 7 and PT = 12, then what is PA?

 

 Dec 30, 2020
 #1
avatar+117546 
+1

We can use  the tangent-secant theorem to solve this

 

PT^2   = AP ( AP + AB)

 

( 12)^2  =  AP^2  +  AP7

 

144  = AP^2  +  7AP      rearrange as

 

AP^2  + 7AP    -  144    =     0          factor as

 

(AP  +16)  (AP - 9)   =  0

 

The first factor set to  0   will give us what we need

 

AP  - 9    =    0

 

AP    =   PA   =  9

 

 

cool cool cool

 Dec 30, 2020
edited by CPhill  Dec 30, 2020
 #3
avatar+1162 
+1

PA must be shorter than PT!!!

jugoslav  Dec 30, 2020
 #4
avatar+117546 
0

OOPS...just a sign error....now our answers agree

 

Thanks for the  correction, jugoslav !!!

 

cool cool cool

CPhill  Dec 30, 2020
 #2
avatar+1162 
+3

A, B, and T are three points lying on a circle.  If PT is a tangent line of the circle and AB = 7 and PT = 12, then what is PA?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

PT2 = PA * PB         PA => x

 

144 = x (x + 7)

 

x2 + 7x - 144 = 0

 

x = 9

 Dec 30, 2020
edited by Guest  Dec 30, 2020

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