IMO 1996 - Shortlisted problems Question 17

G8 (RUS) Let $ABCD$ be a convex quadrilateral, and let $R_A,R_B,R_C,$ and $R_D$ denote the circumradii of the triangles $DAB,ABC,BCD,$ and $CDA$ respectively. Prove that $R_A+R_C\gt R_B+R_D$ if and only if
$$\angle A+\angle C\gt \angle B+\angle D.$$