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3D geo with locus

Source: 43rd International Tournament of Towns, Senior O-Level P4, Fall 2021

February 18, 2023
geometry3D geometryLocusTournament of Towns

Problem Statement

Given is a segment ABAB. Three points X,Y,ZX, Y, Z are picked in the space so that ABXABX is an equilateral triangle and ABYZABYZ is a square. Prove that the orthocenters of all triangles XYZXYZ obtained in this way belong to a fixed circle.
Alexandr Matveev
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