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AD=BE implies ABC right

Source: European Girl's MO 2013, Problem 1

April 10, 2013
geometrycircumcircleTriangleEGMOEGMO 2013

Problem Statement

The side BCBC of the triangle ABCABC is extended beyond CC to DD so that CD=BCCD = BC. The side CACA is extended beyond AA to EE so that AE=2CAAE = 2CA. Prove that, if AD=BEAD=BE, then the triangle ABCABC is right-angled.
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