RIOPLATENSE 1997 Problem 2

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 $ABCD$ at $C$ and tangent to the edges $AA_1$ , $BB _1$ and $DD_ 1$ of the prism. Calculate $r$ .