$\overline{PT}$ is a tangent of circle with centre O at point T. A secant passing through P in at A and B. If P-B-A, PT$=12$ and PB$=4$, then PA ________.

Using the tangent secant theorem, the square of the tangent length equals the product of the external secant segment and the whole secant length. Given PT is 12, PB is 4 and the order of points is P then B then A, the equation is PT squared equals PB multiplied by PA. This gives 12 squared equals 4 multiplied by PA, so 144 equals 4 times PA. Solving this yields PA as 36.

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