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Incentre, circumcentre and midpoints of AC,BC are concyclic

Source: Baltic Way 1999

December 23, 2010
geometryincenterangle bisectorgeometry proposed

Problem Statement

In a triangle ABCABC it is given that 2AB=AC+BC2AB=AC+BC. Prove that the incentre of △ABC\triangle ABC, the circumcentre of △ABC\triangle ABC, and the midpoints of ACAC and BCBC are concyclic.
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