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Angles of obtuse triangle with given lines parallel

Source: South African MO 2014 Q3

October 25, 2014
geometryangle bisectorgeometry unsolved

Problem Statement

In obtuse triangle ABCABC, with the obtuse angle at AA, let DD, EE, FF be the feet of the altitudes through AA, BB, CC respectively. DEDE is parallel to CFCF, and DFDF is parallel to the angle bisector of ∠BAC\angle BAC. Find the angles of the triangle.
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