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A line through incenter bisects a segment.

Source: XVII Sharygin Correspondence Round P7

March 2, 2021
geometryincenterbisects segment

Problem Statement

The incircle of triangle ABCABC centered at II touches CA,ABCA,AB at points E,FE,F respectively. Let points M,NM,N of line EFEF be such that CM=CECM=CE and BN=BFBN=BF. Lines BMBM and CNCN meet at point PP. Prove that PIPI bisects segment MNMN.
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