MathDB
Geometry

Source: Baltic Way 2015

November 8, 2015
geometryBaltic Way

Problem Statement

In triangle ABCABC, the interior and exterior angle bisectors of ∠BAC \angle BAC intersect the line BCBC in DD and EE, respectively. Let FF be the second point of intersection of the line ADAD with the circumcircle of the triangle ABC ABC. Let OO be the circumcentre of the triangle ABC ABC and let D′D' be the reflection of DD in OO. Prove that ∠D′FE=90. \angle D'FE =90.
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