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Proving that five points are coplanar

Source: ToT 2003 SA-6

July 3, 2011
geometry3D geometrytetrahedronparallelograminradiusgeometry unsolved

Problem Statement

Let OO be the center of insphere of a tetrahedron ABCDABCD. The sum of areas of faces ABCABC and ABDABD equals the sum of areas of faces CDACDA and CDBCDB. Prove that OO and midpoints of BC,AD,ACBC, AD, AC and BDBD belong to the same plane.
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