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<BDC when AC\perp BD, <BCA = 10^o,<BDA = 20^o, <BAC = 40^o

Source: 2011 Oral Moscow Geometry Olympiad grades 10-11 p5

April 7, 2020
Angle Chasinganglesperpendiculargeometry

Problem Statement

In a convex quadrilateral ABCD,AC⊥BD,∠BCA=10o,∠BDA=20o,∠BAC=40oABCD, AC\perp BD, \angle BCA = 10^o,\angle BDA = 20^o, \angle BAC = 40^o. Find ∠BDC\angle BDC.
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