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maximum product of inradii by a cevian in equilateral

Source: Korean Mathematical Olympiad 1995, Final Round P3 FKMO

July 21, 2018
geometryinradiusEquilateral Trianglemaximum

Problem Statement

Let ABCABC be an equilateral triangle of side 11, DD be a point on BCBC, and r1,r2r_1, r_2 be the inradii of triangles ABDABD and ADCADC. Express r1r2r_1r_2 in terms of p=BDp = BD and find the maximum of r1r2r_1r_2.
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