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Perpendicular segments

Source: Finnish Mathematics Competition 2008, Final Round, Problem 2

November 14, 2011
geometryincentercircumcirclepower of a pointradical axis

Problem Statement

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