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sum of inradii in terms of side of an equilateral

Source: Austrian-Polish 1993

May 24, 2019
geometryinradiusEquilateral TriangleEquilateralincircle

Problem Statement

Point PP is taken on the extension of side ABAB of an equilateral triangle ABCABC so that AA is between BB and PP. Denote by aa the side length of triangle ABCABC, by r1r_1 the inradius of triangle PACPAC, and by r2r_2 the exradius of triangle PBCPBC opposite PP. Find the sum r1+r2r_1+r_2 as a function in aa.
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