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calculation !

Source: IMO ShortList 1998, geometry problem 7

October 15, 2004
trigonometrygeometrytrapezoidparallelogramIMO Shortlist

Problem Statement

Let ABCABC be a triangle such that ∠ACB=2∠ABC\angle ACB=2\angle ABC. Let DD be the point on the side BCBC such that CD=2BDCD=2BD. The segment ADAD is extended to EE so that AD=DEAD=DE. Prove that ∠ECB+180∘=2∠EBC. \angle ECB+180^{\circ }=2\angle EBC.
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