1958 AHSME Problem 42

In a circle with center O, chord \overline{AB} equals chord \overline{AC}. Chord \overline{AD} cuts \overline{BC} in E. If AC = 12 and AE = 8, then AD equals:

\textbf{(A)}\ 27\qquad \textbf{(B)}\ 24\qquad \textbf{(C)}\ 21\qquad \textbf{(D)}\ 20\qquad \textbf{(E)}\ 18

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