MathDB
Angle EBA is equal to Angle DCB

Source: Baltic Way 2011

November 6, 2011
geometry proposedgeometry

Problem Statement

Let ABCDABCD be a convex quadrilateral such that ∠ADB=∠BDC\angle ADB=\angle BDC. Suppose that a point EE on the side ADAD satisfies the equality AE⋅ED+BE2=CD⋅AE.AE\cdot ED + BE^2=CD\cdot AE. Show that ∠EBA=∠DCB\angle EBA=\angle DCB.
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