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Grid geometry

Source: Kyiv City MO 2023 Round 1, Problem 10.3

December 16, 2023
analytic geometrygridgeometrycyclic quadrilateral

Problem Statement

Consider all pairs of distinct points on the Cartesian plane (A,B)(A, B) with integer coordinates. Among these pairs of points, find all for which there exist two distinct points (X,Y)(X, Y) with integer coordinates, such that the quadrilateral AXBYAXBY is convex and inscribed.
Proposed by Anton Trygub
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