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sphere intersecting planes of tetrahedron in circles - Austrian-Polish 2003

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May 18, 2019
geometry3D geometryspheretetrahedron

Problem Statement

ABCDABCD is a tetrahedron such that we can find a sphere k(A,B,C)k(A,B,C) through A,B,CA, B, C which meets the plane BCDBCD in the circle diameter BCBC, meets the plane ACDACD in the circle diameter ACAC, and meets the plane ABDABD in the circle diameter ABAB. Show that there exist spheres k(A,B,D)k(A,B,D), k(B,C,D)k(B,C,D) and k(C,A,D)k(C,A,D) with analogous properties.
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