1956 AHSME Problem 14

The points A,B,C are on a circle O. The tangent line at A and the secant BC intersect at P, B lying between C and P. If \overline{BC} = 20 and \overline{PA} = 10\sqrt {3}, then \overline{PB} equals:

\textbf{(A)}\ 5 \qquad\textbf{(B)}\ 10 \qquad\textbf{(C)}\ 10\sqrt {3} \qquad\textbf{(D)}\ 20 \qquad\textbf{(E)}\ 30

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.