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convex ABCD, <ADB +<ACB = <CAB + <DBA =30^o, AD=BC, right triangle

Source: SRMC 2010 P1

August 30, 2018
geometryconvex quadrilateralanglesright triangle

Problem Statement

In a convex quadrilateral it is known ABCDABCD that ∠ADB+∠ACB=∠CAB+∠DBA=30∘\angle ADB + \angle ACB = \angle CAB + \angle DBA = 30^{\circ} and AD=BCAD = BC. Prove that from the lengths DBDB, CACA and DCDC, you can make a right triangle.
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