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

Source: Rioplatense Olympiad 1997 level 3 P2

September 4, 2018

geometry3-Dimensional Geometryprismsphererhombus3D geometry

Problem Statement

Consider a prism, not necessarily right, whose base is a rhombus

ABCD

with side

AB = 5

and diagonal

AC = 8

. A sphere of radius

r

is tangent to the plane

ABCD

C

and tangent to the edges

AA_1

BB _1

and

DD_ 1

of the prism. Calculate

r