Canada Math Contest #2 - Problem 8

Let AB be a line segment. Let C and D be on the perpendicular from A to AB, and E be on the perpendicular from B to AB such that BE=CD=2AC=2AB and C, D, E are on the same side as AB. Let AE and BD intersect at F. If \sin^2(\angle AFC) can be written as \frac{p}{q} where p and q are relatively prime positive integers, find p+q.