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Inequality for circumcircle radius of the triangle XYZ

Source: AIMO 2008, TST 5, P2, Suggested by Gunther Vogel

January 4, 2009
inequalitiesgeometrycircumcircletrigonometrygeometry unsolved

Problem Statement

For three points X,Y,Z X,Y,Z let RXYZ R_{XYZ} be the circumcircle radius of the triangle XYZ. XYZ. If ABC ABC is a triangle with incircle centre I I then we have: \frac{1}{R_{ABI}} \plus{} \frac{1}{R_{BCI}} \plus{} \frac{1}{R_{CAI}} \leq \frac{1}{\bar{AI}} \plus{} \frac{1}{\bar{BI}} \plus{} \frac{1}{\bar{CI}}.
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