1991 AHSME Problem 29

Equilateral triangle ABC has P on AB and Q on AC. The triangle is folded along PQ so that vertex A now rests at A' on side BC. If BA'=1 and A'C=2 then the length of the crease PQ is

\textbf{(A) } \frac{8}{5} \qquad \textbf{(B) } \frac{7}{20}\sqrt{21} \qquad \textbf{(C) } \frac{1+\sqrt{5}}{2} \qquad \textbf{(D) } \frac{13}{8} \qquad \textbf{(E) } \sqrt{3}

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