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Show that middle point of line segment lies on line

Source: 67 Polish MO 2016 Second Round - Problem 5

April 30, 2018
geometrycirclePolandquadrilateralcyclic quadrilateral

Problem Statement

Quadrilateral ABCDABCD is inscribed in circle. Points PP and QQ lie respectively on rays AB→AB^{\rightarrow} and AD→AD^{\rightarrow} such that AP=CDAP = CD, AQ=BCAQ = BC. Show that middle point of line segment PQPQ lies on the line ACAC.
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