AHSME 1961 Problem 11

Two tangents are drawn to a circle from an exterior point $A$; they touch the circle at points $B$ and $C$ respectively. A third tangent intersects segment $AB$ in $P$ and $AC$ in $R$, and touches the circle at $Q$. If $AB=20$, then the perimeter of $\triangle APR$ is $\textbf{(A)}\ 42 \textbf{(B)}\ 40.5 \textbf{(C)}\ 40 \textbf{(D)}\ 39\frac{7}{8} \textbf{(E)}\ \text{not determined by the given information}$