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Easy geometry

Source: China South East Mathematical Olympiad 2016 Grade 10 Prob. 7

July 31, 2016
geometryincenter

Problem Statement

II is incenter of △ABC\triangle{ABC}. The incircle touches BC,CA,ABBC,CA,AB at D,E,FD,E,F, respectively . Let M,N,K=BI,CI,DI∩EFM,N,K=BI,CI,DI \cap EF respectively and BN∩CM=P,AK∩BC=GBN\cap CM=P,AK\cap BC=G. Point QQ is intersection of the perpendicular line to PGPG through II and the perpendicular line to PBPB through PP. Prove that BIBI bisect segment PQPQ.
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