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Two isosceles triangles become equilateral

Source: Romanian TST 1 2006, Problem 1

April 19, 2006
geometrycircumcirclegeometric transformationrotationsimilar trianglescomplex numbersgeometry proposed

Problem Statement

Let ABCABC and AMNAMN be two similar triangles with the same orientation, such that AB=ACAB=AC, AM=ANAM=AN and having disjoint interiors. Let OO be the circumcenter of the triangle MABMAB. Prove that the points OO, CC, NN, AA lie on the same circle if and only if the triangle ABCABC is equilateral. Valentin Vornicu
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