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intersection of perp. diagonals lies on XY (2022 Novosibirsk Oral Geo Oly 8.7)

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September 2, 2023
geometryconcurrencyconcurrent

Problem Statement

The diagonals of the convex quadrilateral ABCDABCD intersect at the point OO. The points XX and YY are symmetrical to the point OO with respect to the midpoints of the sides BCBC and ADAD, respectively. It is known that AB=BC=CDAB = BC = CD. Prove that the point of intersection of the perpendicular bisectors of the diagonals of the quadrilateral lies on the line XYXY.
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