KöMaL 2008 A449

In the convex quadrilateral ABCD , denote by $r_A$, $r_B$, $r_C$ and $r_D$ the inradii of triangles BCD , CDA , DAB and ABC , respectively. Prove that the quadrilateral ABCD is cyclic if and only if $r_A$+$r_C$=$r_B$+$r_D$.