MathDB
perpendicular wanted, cyclic ABCD, BC=DFC, AB=AC, arc midpoint

Source: Champions Tournament (Ukraine) - Турнір чемпіонів - 2019 Seniors p2

September 2, 2020
geometryperpendicularequal segmentscyclic quadrilateralarc midpointChampions Tournament

Problem Statement

The quadrilateral ABCDABCD is inscribed in the circle and the lengths of the sides BCBC and DCDC are equal, and the length of the side ABAB is equal to the length of the diagonal ACAC. Let the point PP be the midpoint of the arc CDCD, which does not contain point AA, and QQ is the point of intersection of diagonals ACAC and BDBD. Prove that the lines PQPQ and ABAB are perpendicular.
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