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equal diagonals in ABCD and a few perpendicular bisectors

Source: Sharygin Geometry Olympiad 2016 Final Round problem 7 grade 8

July 22, 2018
geometryperpendicular bisectordiagonals

Problem Statement

Diagonals of a quadrilateral ABCDABCD are equal and meet at point OO. The perpendicular bisectors to segments ABAB and CDCD meet at point PP, and the perpendicular bisectors to BCBC and ADAD meet at point QQ. Find angle POQ\angle POQ.
by A.Zaslavsky