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orthocenter, incenter and circumcenter of triangle revisited

Source: Vietnam TST 1993 for the 34nd IMO, problem 4

June 25, 2005
geometryincentercircumcircleinequalitiesEulerratioangle bisector

Problem Statement

Let HH, II, OO be the orthocenter, incenter and circumcenter of a triangle. Show that 2⋅IO≥IH2 \cdot IO \geq IH. When does the equality hold ?
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