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NM tangent to incircle of ABC, 2 circumcircles related

Source: IX - Mathematics Regional Olympiad of Mexico Northeast 2009 P3

September 17, 2022
geometryincircletangentcircumcircle

Problem Statement

The incircle of triangle △ABC\vartriangle ABC is tangent to side ABAB at point PP and to side BCBC at point QQ. The circle passing through points A,P,QA,P,Q intersects line BCBC a second time at MM and the circle passes through the points C,P,QC,P,Q and cuts the line ABAB a second time at pointN N. Prove that NMNM is tangent to the incircle of ABCABC.
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