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Isosceles triangles constructed on the sides of a triangle

Source: Czech-Polish-Slovak 2001 Q2

April 30, 2013
geometrycircumcircleperimetergeometric transformationreflectionparallelogramgeometry unsolved

Problem Statement

A triangle ABCABC has acute angles at AA and BB. Isosceles triangles ACDACD and BCEBCE with bases ACAC and BCBC are constructed externally to triangle ABCABC such that ∠ADC=∠ABC\angle ADC = \angle ABC and ∠BEC=∠BAC\angle BEC = \angle BAC. Let SS be the circumcenter of △ABC\triangle ABC. Prove that the length of the polygonal line DSEDSE equals the perimeter of triangle ABCABC if and only if ∠ACB\angle ACB is right.
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