Geometry Practice Test 6

PT is a tangent and AB is a chord of circle of 18 cm. and PT = 2AP
We have
$\mathit{P}{\mathit{T}}^2$ = PA.PB
${\left(2\mathit{A}\mathit{P}\right)}^2$ = PA.PB
$4\mathit{A}{\mathit{P}}^2$ = AP.PB
4AP = PB
4AP = PA + AB
4AP − AP = 18
3AP = 18

AP = $\frac{18}{3}$ = 6 cm
$\mathit{P}{\mathit{T}}^2$ = 6.18
PT = $\sqrt{24\times 8}$
PT = 12 units