Let be a convex quadrilateral, and let denote the circumradii of the triangles respectively. Prove that if and only if
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Let $ABCD$ be a convex quadrilateral, and let $R_A, R_B, R_C, R_D$ denote the circumradii of the triangles $DAB, ABC, BCD, CDA,$ respectively. Prove that $R_A + R_C > R_B + R_D$ if and only if $\angle A + \angle C > \angle B + \angle D.$
Source: Međunarodna matematička olimpijada, shortlist 1996
Školjka 
be a convex quadrilateral, and let 
denote the circumradii of the triangles 
respectively. Prove that 
if and only if 