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Ratio of circumcircle radius to incircle diameter

Source: AIMO 2007, TST 6, P3

January 11, 2009
ratiogeometrycircumcirclegeometry unsolved

Problem Statement

In triangle ABC ABC we have a≥b a \geq b and a≥c. a \geq c. Prove that the ratio of circumcircle radius to incircle diameter is at least as big as the length of the centroidal axis sa s_a to the altitude aa. a_a. When do we have equality?
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