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r_1 + r_2> r, inradii

Source: 2009 Indonedia MO Province P2 q3 OSP

December 11, 2020
geometrygeometric inequality

Problem Statement

Given triangle ABCABC and point DD on the ACAC side. Let r1,r2r_1, r_2 and rr denote the radii of the incircle of the triangles ABD,BCDABD, BCD, and ABCABC, respectively. Prove that r1+r2>rr_1 + r_2> r.
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