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sum of inradii of AMB , AMC (V Soros Olympiad 1998-99 Round 3 10.5)

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May 26, 2024
geometryinradius

Problem Statement

The radius of the circle inscribed in triangle ABCABC is equal to rr. This circle is tangent to BCBC at point MM and divides the segment AMAM in ratio kk (starting from vertex AA). Find the sum of the radii of the circles inscribed in triangles AMBAMB and AMCAMC.