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20

Part of 2005 Sharygin Geometry Olympiad

Problems(1)

circumsphere lies entirely inside another circumsphere, tetrahedra related

Source: Sharygin 2005 XI CR 20

8/19/2019
Let II be the center of the sphere inscribed in the tetrahedron ABCD,A′,B′,C′,D′ABCD, A ', B', C ', D' be the centers of the spheres circumscribed around the tetrahedra IBCD,ICDA,IDAB,IABCIBCD, ICDA, IDAB, IABC, respectively. Prove that the sphere circumscribed around ABCDABCD lies entirely inside the circumscribed around A′B′C′D′A'B'C'D '.
3D geometrytetrahedronspheregeometry