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inequality on radius

Source: 9th-th Hungary-Israel Binational Mathematical Competition 1998

July 13, 2007
inequalitiestrigonometrygeometrycircumcirclegeometry proposed

Problem Statement

A triangle ABC is inscribed in a circle with center O O and radius R R. If the inradii of the triangles OBC,OCA,OAB OBC, OCA, OAB are r1,r2,r3 r_{1}, r_{2}, r_{3} , respectively, prove that 1r1+1r2+1r3≥43+6R. \frac{1}{r_{1}}+\frac{1}{r_{2}}+\frac{1}{r_{3}}\geq\frac{4\sqrt{3}+6}{R}.
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