MathDB

M2545

Part of Kvant 2019

Problems(1)

Isotomic points on line joining incenters

Source: International Zhautykov Olympiad 2018/2

1/12/2018
Let N,K,LN,K,L be points on the sides AB‾,BC‾,CA‾\overline{AB}, \overline{BC}, \overline{CA} respectively. Suppose AL=BKAL=BK and CN‾\overline{CN} is the internal bisector of angle ACBACB. Let PP be the intersection of lines AK‾\overline{AK} and BL‾\overline{BL} and let I,JI,J be the incenters of triangles APLAPL and BPKBPK respectively. Let QQ be the intersection of lines IJ‾\overline{IJ} and CN‾\overline{CN}. Prove that IP=JQIP=JQ.
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