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AB//CD when <B= 2<A , angle bisector of B intersects perp.bisector of AC at D

Source: 2010 VWO Flanders MO p3

August 7, 2020
geometryangle bisectorparallelperpendicularangles

Problem Statement

In a triangle ABCABC, ∠B=2∠A≠90o\angle B= 2\angle A \ne 90^o . The inner bisector of BB intersects the perpendicular bisector of [AC][AC] at a point DD. Prove that AB∥CDAB \parallel CD.
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