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perimeter of triangles inequality, isosceles (2012 Kyiv City MO 7.4)

Source:

August 3, 2020
geometryperimeterisoscelesgeometric inequality

Problem Statement

Given an isosceles triangle ABCABC with a vertex at the point BB. Based on ACAC, an arbitrary point DD is selected, different from the vertices AA and CC . On the line ACAC select the point EE outside the segment ACAC, for which AE=CDAE = CD. Prove that the perimeter ΔBDE\Delta BDE is larger than the perimeter ΔABC\Delta ABC.
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