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Three concurrent lines

Source: Baltic Way 2000 Problem 3

February 13, 2009
geometrycircumcircletrigonometrygeometry unsolved

Problem Statement

Given a triangle ABC ABC with \angle A \equal{} 90^{\circ} and AB≠AC AB \neq AC. The points D D, E E, F F lie on the sides BC BC, CA CA, AB AB, respectively, in such a way that AFDE AFDE is a square. Prove that the line BC BC, the line FE FE and the line tangent at the point A A to the circumcircle of the triangle ABC ABC intersect in one point.
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