AHSME 1961 Problem 38

$\triangle ABC$ is inscribed in a semicircle of radius $r$ so that its base $AB$ coincides with diameter $AB$. Point $C$ does not coincide with either $A$ or $B$. Let $s=AC+BC$. Then, for all permissible positions of $C$: $\textbf{(A)}\ s^2\le8r^2 \textbf{(B)}\ s^2=8r^2 \textbf{(C)}\ s^2 \ge 8r^2 \\ \textbf{(D)}\ s^2\le4r^2 \textbf{(E)}\ s^2=4r^2$