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MMO 215 Moscow MO 1952 inequality with inradii

Source:

August 8, 2019
geometryincircleinradiusgeometric inequality

Problem Statement

△ABC\vartriangle ABC is divided by a straight line BDBD into two triangles. Prove that the sum of the radii of circles inscribed in triangles ABDABD and DBCDBC is greater than the radius of the circle inscribed in △ABC\vartriangle ABC.
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