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Perpendicularity

Source: Finnish Mathematics Competition 2003, Final Round, Problem 1

November 14, 2011
geometryincentercircumcirclegeometry unsolved

Problem Statement

The incentre of the triangle ABCABC is I.I. The rays AI,BIAI, BI and CICI intersect the circumcircle of the triangle ABCABC at the points D,ED, E and F,F, respectively. Prove that ADAD and EFEF are perpendicular.
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