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Midpoint on circumcircle

Source: Sharygin 2019 finals Day 1 Grade 8 P1

July 30, 2019
geometrySharygin Geometry Olympiadcircumcircle

Problem Statement

A trapezoid with bases ABAB and CDCD is inscribed into a circle centered at OO. Let APAP and AQAQ be the tangents from AA to the circumcircle of triangle CDOCDO. Prove that the circumcircle of triangle APQAPQ passes through the midpoint of ABAB.
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