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Geometry Problem

Source: 1989 National High School Mathematics League, Exam Two, Problem 1

February 25, 2020
geometry

Problem Statement

In △ABC\triangle ABC, AB>ACAB>AC, bisector of outer angle ∠A\angle A intersects circumcircle of △ABC\triangle ABC at EE. Projection of EE on ABAB is FF. Prove that 2AF=AB−AC2AF=AB-AC.
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