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ASU 440 All Soviet Union MO 1986 sum of angles of tetrahedron fixed

Source:

August 7, 2019
geometry3D geometryspheretetrahedronfixedanglesSum

Problem Statement

Consider all the tetrahedrons AXBYAXBY, circumscribed around the sphere. Let AA and BB points be fixed. Prove that the sum of angles in the non-plane quadrangle AXBYAXBY doesn't depend on points XX and YY .
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