2002 Cayley Problem 18

In the diagram, triangle ABC is isosceles with AB = AC, and AG is perpendicular to BC. Point D is the midpoint of AB, point F is the midpoint of AC, and E is the point of intersection of DF and AG. What fraction of the area of \triangle ABC does the shaded area represent?

\textbf{(A)}\ \frac{1}{12}\quad \textbf{(B)}\ \frac{1}{6}\quad \textbf{(C)}\ \frac{1}{4}\quad \textbf{(D)}\ \frac{1}{10}\quad \textbf{(E)}\ \frac{1}{8}

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Full credit to this problem is given to the CEMC, you may view all Cayley contests here.