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Geometric inequality 1

Source: Bosnia - Herzegovina Mathematical Olympiad 2002, APMC 1981

December 13, 2003
inequalitiesgeometrytrigonometryinequalities solved

Problem Statement

Given is a triangle ABCABC, the inscribed circle GG of which has radius rr. Let rar_a be the radius of the circle touching ABAB, ACAC and GG. [This circle lies inside triangle ABCABC.] Define rbr_b and rcr_c similarly. Prove that ra+rb+rc≥rr_a + r_b + r_c \geq r and find all cases in which equality occurs. Bosnia - Herzegovina Mathematical Olympiad 2002
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