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Geometry / Incicles and Incenters

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August 11, 2019
geometryincircleIncentersincenter

Problem Statement

Let ABCABC be a triangle with sides 51,52,5351, 52, 53. Let Ω\Omega denote the incircle of △ABC\bigtriangleup ABC. Draw tangents to Ω\Omega which are parallel to the sides of ABCABC. Let r1,r2,r3r_1, r_2, r_3 be the inradii of the three corener triangles so formed, Find the largest integer that does not exceed r1+r2+r3r_1 + r_2 + r_3.
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