MathDB
Lines pass through incenter and excenter

Source: 2005 China Second Round Olympiad

September 2, 2014
geometryincentercircumcircle

Problem Statement

In ABC\triangle ABC, AB>ACAB>AC, ll is a tangent line of the circumscribed circle of ABC\triangle ABC, passing through AA. The circle, centered at AA with radius ACAC, intersects ABAB at DD, and line ll at E,FE, F. Prove that lines DE,DFDE, DF pass through the incenter and an excenter of ABC\triangle ABC respectively.