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sum of inradii = altitude

Source: Polish MO second round 1951 p1

August 28, 2024
geometryincirclesincircleright triangle

Problem Statement

In a right triangle ABC ABC , the altitude CD CD is drawn from the vertex of the right angle C C and a circle is inscribed in each of the triangles ABC ABC , ACD ACD and BCD BCD . Prove that the sum of the radii of these circles equals the height CD CD .
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