1962 AHSME Problem 23

In \triangle ABC, CD is the altitude to AB and AE is the altitude to BC. If the lengths of AB, CD, and AE are known, the length of DB is:

\begin{array}{l} \textbf{(A)}\ \text{not determined by the information given} \qquad \\ \textbf{(B)}\ \text{determined only if A is an acute angle} \qquad \\ \textbf{(C)}\ \text{determined only if B is an acute angle} \qquad \\ \textbf{(D)}\ \text{determined only if ABC is an acute triangle} \qquad \\ \textbf{(E)}\ \text{none of these is correct} \end{array}

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