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Circum centre of triangle and orthocentre Parallel

Source: INMO 2014- Problem 5

February 2, 2014
geometrycircumcirclegeometric transformationreflectiontrigonometryperpendicular bisectorgeometry proposed

Problem Statement

In a acute-angled triangle ABCABC, a point DD lies on the segment BCBC. Let O1,O2O_1,O_2 denote the circumcentres of triangles ABDABD and ACDACD respectively. Prove that the line joining the circumcentre of triangle ABCABC and the orthocentre of triangle O1O2DO_1O_2D is parallel to BCBC.
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