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bisector of <BAC _|_AD, trapezium, AB = BE, AC = DE NZMO 2021 R1 p2

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September 20, 2021
geometryangle bisectortrapezoidperpendicular

Problem Statement

Let ABCDABCD be a trapezium such that AB∥CDAB\parallel CD. Let EE be the intersection of diagonals ACAC and BDBD. Suppose that AB=BEAB = BE and AC=DEAC = DE. Prove that the internal angle bisector of ∠BAC\angle BAC is perpendicular to ADAD.
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