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Concurrent circles

Source: Indonesia Mathematics Olympiad 2008 Day 1 Problem 1

August 13, 2008
geometrycircumcirclegeometric transformationrotationgeometry proposed

Problem Statement

Given triangle ABC ABC. Points D,E,F D,E,F outside triangle ABC ABC are chosen such that triangles ABD ABD, BCE BCE, and CAF CAF are equilateral triangles. Prove that cicumcircles of these three triangles are concurrent.
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