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concurrency related to a trapezoid and a circle

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p3

April 7, 2020
geometrytrapezoidconcurrencyconcurrentcircle

Problem Statement

A non-isosceles trapezoid ABCDABCD (AB//CDAB // CD) is given. An arbitrary circle passing through points AA and BB intersects the sides of the trapezoid at points PP and QQ, and the intersect the diagonals at points MM and NN. Prove that the lines PQ,MNPQ, MN and CDCD are concurrent.
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