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sum of AI less than 3R

Source: Moldova 2007 IMO-BMO TST II problem 2

March 23, 2007
geometryincentercircumcircletrigonometryinequalitiestrig identitiesLaw of Sines

Problem Statement

If II is the incenter of a triangle ABCABC and RR is the radius of its circumcircle then AI+BI+CI≤3RAI+BI+CI\leq 3R
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