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Inequalituy with the incenter [Iran Second Round 1991]

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November 30, 2010
geometryincentercircumcircleinequalitiesgeometry proposed

Problem Statement

Triangle ABCABC is inscribed in circle C.C. The bisectors of the angles A,BA,B and CC meet the circle CC again at the points A′,B′,C′A', B', C'. Let II be the incenter of ABC,ABC, prove that IA′IA+IB′IB+IC′IC≥3\frac{IA'}{IA} + \frac{IB'}{IB}+\frac{IC'}{IC} \geq 3,IA′+IB′+IC′≥IA+IB+IC, IA'+IB'+IC' \geq IA+IB+IC
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