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Part of 1997 Rioplatense Mathematical Olympiad, Level 3

Problems(1)

sphere tangent to plane of rhombus ABCD and to 3 edges of a prism with base ABCD

Source: Rioplatense Olympiad 1997 level 3 P2

9/4/2018
Consider a prism, not necessarily right, whose base is a rhombus ABCDABCD with side AB=5AB = 5 and diagonal AC=8AC = 8. A sphere of radius rr is tangent to the plane ABCDABCD at CC and tangent to the edges AA1AA_1 , BB1BB _1 and DD1DD_ 1 of the prism. Calculate rr .
geometry3-Dimensional Geometryprismsphererhombus3D geometry