AHSME 1974 Problem 23

In the adjoining figure $TP$ and $T'Q$ are parallel tangents to a circle of radius $r$, with $T$ and $T'$ the points of tangency. $PT''Q$ is a third tangent with $T'''$ as a point of tangency. If $TP=4$ and $T'Q=9$ then $r$ is

$\mathrm{(A)\ } 25/6 \mathrm{(B) \ } 6 \mathrm{(C) \ } 25/4$ $\mathrm{(D) \ } \text{a number other than }25/6, 6, 25/4$ $\mathrm{(E) \ }\text{not determinable from the given information}$