MathDB
Triangle

Source: Iranian National Olympiad (3rd Round) 2006

September 21, 2006
geometryincentertrigonometrycircumcircleparallelogramgeometry proposed

Problem Statement

MM is midpoint of side BCBC of triangle ABCABC, and II is incenter of triangle ABCABC, and TT is midpoint of arc BCBC, that does not contain AA. Prove that cos⁡B+cos⁡C=1⟺MI=MT\cos B+\cos C=1\Longleftrightarrow MI=MT
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