1951 AHSME 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\qquad\textbf{(B)}\ \text{equal to }AB\sqrt{2}\qquad\textbf{(C)}\ \geq AB\sqrt{2}\qquad\textbf{(D)}\ \leq AB\sqrt{2} \qquad \textbf{(E)}\ AB^{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.