1975 AHSME Problem 24

In \triangle ABC, \measuredangle C=\theta and \measuredangle B=2\theta, where 0^{\circ} <\theta < 60^{\circ}. The circle with center A and radius AB intersects AC at D and intersects BC, extended if necessary, at B and at E (E may coincide with B). Then EC=AD

\begin{array}{l} \textbf{(A)}\ \text{for no values of}\ \theta \qquad \textbf{(B)}\ \text{only if}\ \theta=45^{\circ} \qquad \textbf{(C)}\ \text{only if}\ 0^{\circ}<\theta\le 45^{\circ}\\ \qquad\ \textbf{(D)}\ \text{only if}\ 45^{\circ}\le\theta < 60^{\circ}\qquad \textbf{(E)}\ \text{for all}\ \theta\ \text{such that}\ 0^{\circ}<\theta < 60^{\circ} \end{array}

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