Cool Geometry!

Geometry Level 2

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.


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