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# stuck on this

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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
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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   Dec 30, 2020
edited by CPhill  Dec 30, 2020
#3
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PA must be shorter than PT!!!

jugoslav  Dec 30, 2020
#4
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OOPS...just a sign error....now our answers agree

Thanks for the  correction, jugoslav !!!   CPhill  Dec 30, 2020
#2
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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?

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PT2 = PA * PB         PA => x

144 = x (x + 7)

x2 + 7x - 144 = 0

x = 9

Dec 30, 2020
edited by Guest  Dec 30, 2020