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A Relation between Incircles and Excircles

Let ABC be a triangle and M be a point on BC. Let , , and be the radii of the incircles of the triangles ACM, ABM, and ABC and let , , and be the radii of the corresponding excircles tangent to BC. Then .

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This is problem 1 from the 12-th International Mathematical Olympiad.

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"A Relation between Incircles and Excircles" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/ARelationBetweenIncirclesAndExcircles/
Contributed by: Jay Warendorff
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