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coplanar touchpoints of tetrahedron and sphere

Source: Polish MO Finals 1964 p3

August 30, 2024
geometry3D geometrytetrahedronsphere

Problem Statement

Given a tetrahedron ABCD ABCD whose edges AB,BC,CD,DA AB, BC, CD, DA are tangent to a certain sphere. Prove that the points of tangency lie in the same plane.
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