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perpendicular wanted, circumcircle and perpendicular related

Source: 2016 Saudi Arabia IMO TST , level 4, II p2

July 27, 2020
geometrycircleperpendicularcircumcircle

Problem Statement

Let ABCABC be a triangle inscribed in the circle (O)(O) and PP is a point inside the triangle ABCABC. Let DD be a point on (O)(O) such that AD⊥APAD \perp AP. The line CDCD cuts the perpendicular bisector of BCBC at MM. The line ADAD cuts the line passing through BB and is perpendicular to BPBP at QQ. Let NN be the reflection of QQ through MM. Prove that CN⊥CPCN \perp CP.
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