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A Relation between Incircles and Excircles

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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 .

Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA

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

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