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Geometry

Source: 2005 National High School Mathematics League, Exam Two, Problem 1

March 20, 2020
geometry

Problem Statement

In ABC\triangle ABC, AB>ACAB>AC, ll is tangent line of the circumscribed circle of ABC\triangle ABC that passes AA. The circle with center AA and radius ACAC, intersects segment ABAB at DD, and line ll at E,FE, F (F,BF,B are on the same side). Prove that lines DE,DFDE, DF pass the incenter and an excenter of ABC\triangle ABC respectively.