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prove that a tetrahedron given lengths has both sphere inside and around it

Source: Tuymaada 1996 p8

April 27, 2019
geometry3D geometrysolid geometrytetrahedronsphere

Problem Statement

Given a tetrahedron ABCDABCD, in which AB=CD=13,AC=BD=14AB=CD= 13 , AC=BD=14 and AD=BC=15AD=BC=15. Show that the centers of the inscribed sphere and sphere around it coincide, and find the radii of these spheres.