stuck on this

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

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