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IMO Shortlist 2014 G2

Source:

July 11, 2015
IMO Shortlistgeometry

Problem Statement

Let ABCABC be a triangle. The points K,L,K, L, and MM lie on the segments BC,CA,BC, CA, and AB,AB, respectively, such that the lines AK,BL,AK, BL, and CMCM intersect in a common point. Prove that it is possible to choose two of the triangles ALM,BMK,ALM, BMK, and CKLCKL whose inradii sum up to at least the inradius of the triangle ABCABC.
Proposed by Estonia
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