IMO Shortlist 1996 problem G8


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2. travnja 2012.
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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.
Izvor: Međunarodna matematička olimpijada, shortlist 1996