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isosceles trapezoid with 3 equal sides

Source: JBMO Shortlist 2005

October 13, 2017
JBMOgeometrytrapezoid

Problem Statement

Let ABCDABCD be an isosceles trapezoid with AB=AD=BC,AB//CD,AB>CDAB=AD=BC, AB//CD, AB>CD. Let E=AC∩BDE= AC \cap BD and NN symmetric to BB wrt ACAC. Prove that the quadrilateral ANDEANDE is cyclic.
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