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S is the incenter of triangle ABC

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September 19, 2010
geometryincentercircumcircleinequalities

Problem Statement

Let SS be the incenter of triangle ABCABC. A1,B1,C1A_1, B_1, C_1 are the intersections of AS,BS,CSAS, BS, CS with the circumcircle of triangle ABCABC respectively. Prove that SA1+SB1+SC1≥SA+SB+SC.SA_1 + SB_1 + SC_1 \geq SA + SB + SC.
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