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Perpendicular lines due to circle

Source: Germany 2016 - BWM Round 1, #3

November 12, 2016
geometrygeometry unsolvedperpendicularcirclechordGermany

Problem Statement

Let A,B,CA,B,C and DD be points on a circle in this order. The chords ACAC and BDBD intersect in point PP. The perpendicular to ACAC through C and the perpendicular to BDBD through DD intersect in point QQ. Prove that the lines ABAB and PQPQ are perpendicular.
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