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PQ _|_ AC wanted, arc midpoint of circumcircle related

Source: 2019 XXIV All-Ukrainian Correspondence MO grades 5-12 p11

April 29, 2021
geometryperpendiculararc midpointUkraine Correspondence

Problem Statement

Let OO be the center of the circle circumscribed around the acute triangle ABCABC, and let NN be the midpoint of the arc ABCABC of this circle. On the sides ABAB and BCBC mark points DD and EE respectively, such that the point OO lies on the segment DEDE. The lines DNDN and BCBC intersect at the point PP, and the lines ENEN and ABAB intersect at the point QQ. Prove that PQ⊥ACPQ \perp AC.
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