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 solution barring algebraic screw-up by xdog)

That works out with Geometers' Sketchpad. That is, the sum of what's given for M+N+p+q+r agrees with the area of the whole triangle ABC.

Posted by Charlie on 2008-12-01 03:42:52