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The South African Mathematical Olympiad 2007

Source: Problem 3

August 22, 2008
geometryincentergeometry proposed

Problem Statement

In acute-angled triangle ABC ABC, the points D,E,F D,E,F are on sides BC,CA,AB BC,CA,AB, respectively such that \angle AFE \equal{} \angle BFD, \angle FDB \equal{} \angle EDC, \angle DEC \equal{} \angle FEA. Prove that AD AD is perpendicular to BC BC.
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