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Geometry with qual inradii

Source: Kvant Magazine No. 4 2021 M2648

March 9, 2023
geometryinradiusKvant

Problem Statement

The triangle ABCABC is given. Consider the point C′C'{} on the side ABAB such that the segment CC′CC' divides the triangle into two triangles with equal radii of inscribed circles. Denote by tct_c the length of the segment CC′CC'. Similarly, we define tat_a and tbt_b. Express the area of triangle ABCABC in terms of ta,tbt_a,t_b and tct_c.
Proposed by K. Mosevich
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