AHSME 1951 Problem 32

If $\triangle ABC$ is inscribed in a semicircle whose diameter is $AB$, then $AC+BC$ must be $\textbf{(A)}\ \text{equal to }AB \textbf{(B)}\ \text{equal to }AB\sqrt{2} \textbf{(C)}\ \geq AB\sqrt{2} \textbf{(D)}\ \leq AB\sqrt{2}$ $\textbf{(E)}\ AB^{2}$