MathDB
Problem by IZhO 2010

Source:

September 3, 2010
geometryincentertrigonometryinequalitiesEulergeometry proposed

Problem Statement

Let ABCABC arbitrary triangle (AB≠BC≠AC≠ABAB \neq BC \neq AC \neq AB) And O,I,H it's circum-center, incenter and ortocenter (point of intersection altitudes). Prove, that 1) ∠OIH>900\angle OIH > 90^0(2 points) 2)∠OIH>1350\angle OIH >135^0(7 points)
balls for 1) and 2) not additive.
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