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line through N perpendicular to PC crosses a fixed point as P moves along EF

Source: Mathley 2014.1 p6

August 19, 2020
fixedFixed pointgeometryincircle

Problem Statement

Let the inscribed circle (I)(I) of the triangle ABCABC, touches CA,ABCA, AB at E,FE, F. PP moves along EFEF, PBPB cuts CACA at M,MIM, MI cuts the line, through CC perpendicular to ACAC, at NN. Prove that the line through NN is perpendicular to PCPC crosses a fixed point as PP moves.
Tran Quang Hung, High School of Natural Sciences, Hanoi National University
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