Problem

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

Tags: geometry, 3D geometry, Locus, Tournament of Towns



Given is a segment $AB$. Three points $X, Y, Z$ are picked in the space so that $ABX$ is an equilateral triangle and $ABYZ$ is a square. Prove that the orthocenters of all triangles $XYZ$ obtained in this way belong to a fixed circle. Alexandr Matveev