In the figure below, given a triangle
ABC of area S, construct the excircles with
excenters P, Q, and R. Let be D, E, F, G, H,
and M the tangent
points of triangle ABC with its excircles. If S1, S2, S3, S4, S5,
and S6 are
the areas of the triangles AMR, BFR, BEP, CHP, CGQ, and ADQ
respectively, prove that S1 = S2 = S3 = S4
= S5 = S6 = S/2.
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