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inradius wanted, circles tangents to incircle and 2 triangle sides

Source: 2020-21 IOQM p23

January 18, 2021
geometryinradiustangent circles

Problem Statement

The incircle Γ\Gamma of a scalene triangle ABCABC touches BCBC at D,CAD, CA at EE and ABAB at FF. Let rAr_A be the radius of the circle inside ABCABC which is tangent to Γ\Gamma and the sides ABAB and ACAC. Define rBr_B and rCr_C similarly. If rA=16,rB=25r_A = 16, r_B = 25 and rC=36r_C = 36, determine the radius of Γ\Gamma.
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