$20 \cdot 107$ As shown, every point on circle $O'$ is outside circle $O$. Let $P$ and $Q$ be the intersection points of an inner common tangent and two outer common tangents. Then the length of $PQ$ is
(A) the average of the lengths of the inner and outer common tangents.
(B) equal to the length of an outer common tangent if and only if circles $O$ and $O'$ have equal radii.
(C) always equal to the length of an outer common tangent.
(D) greater than the length of an outer common tangent.
(E) the geometric mean of the lengths of the inner and outer common tangents.
[Solution] As shown in the figure, let $X, Y, V$ and $W$ be the points of tangency of the external common tangents, and $R$ and $S$ be the points of tangency of the internal common tangents. By the properties of tangents, we have
$$
\begin{aligned}
P R=P X, & P S=P Y, \\
Q S=Q W, & Q R=Q V .
\end{aligned}
$$

Therefore, $P R+P S+Q S+Q R$
$$
=P X+P Y+Q W+Q V \text {. }
$$

Since $X Y=V W$, and $P Q=X Y=$ $V W$,
then $2 P Q=X Y+V W$.
Thus, the correct choice is $(C)$.