Let ABC be any triangle. Let D be a point on side AB and let E be a point on side AC. Draw lines CD and BE and call their intersection F. Triangle ABC is then divided into three smaller triangles BDF, CEF, BCF and a quadrilateral ADFE.
Let the area of BDF equal r, the area of CEF equal q, and the area of BCF equal p. Express the area of the whole triangle ABC in terms of p, q, and r.
(In reply to computer aided solution
Wow, that is one ugly expression. I tried using coordinate geometry when I first saw this problem, but gave up when trying to create expressions for the three smaller triangles.
I solved this problem by creating some ratios of areas and solving the resulting equations. The end result does not have any square roots or trig functions.