Let $\displaystyle P$ be a point outside a given circle $\displaystyle q$, let $\displaystyle PT$ be a straight line, and let $\displaystyle PAB$ be a secant with chord $\displaystyle AB$. Then, if $\displaystyle PA \cdot PB = PT^{2}$, then $\displaystyle PT$ is tangent to circle $\displaystyle q$.

The converse of this is not hard to prove, but I'm stuck on proving that statement.