Let P be an interior point of a triangle ABC and let BP and CP meet AC and AB in E and F respectively. If [BPF] = 4, [BPC] = 8 and [CPE] = 13, find [AFPE].
(Here [·] denotes the area of a triangle or a quadrilateral, as the case may be.)
The question is adapted from RMO 1997.
Please post your solution/approach to the problem.