20.51 From a point $A$ outside a circle, two tangents $A B$, $A C$ are drawn to the circle, touching it at $B, C$. A third tangent intersects $A B$ at $P$ and $A C$ at $R$, touching the circle at $Q$. If $A B=$ 20, then the perimeter of $\triangle A P R$ is 
(A) 42.
(B) 40.5.
(C) 40.
(D) $39 \frac{7}{8}$.
(E) Cannot be determined.
(12th American High School Mathematics Examination, 1961)
[Solution] Let $p$ be the perimeter of $\triangle A P R$, then
$$
p=A P+P Q+Q R+R A \text {, }
$$

By the given conditions and the properties of tangents, we have $P B=P Q$, and $R Q=R C$, and $A B=A C$.
Therefore,
$$
\begin{aligned}
p & =A P+P B+C R+R A \\
& =A B+A C=2 A B \\
& =40 .
\end{aligned}
$$

Hence, the answer is $(C)$.