PL-OM 2013 Problem 3

Given is a quadrilateral $ABCD$ in which we can inscribe circle. The segments $AB, BC, CD$ and $DA$ are the diameters of the circles $o1, o2, o3$ and $o4$ , respectively. Prove that there exists a circle tangent to all of the circles $o1, o2, o3$ and $o4$ .