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An isosceles trapezium with AB || CD

Source: VAIMO 2008, Problem 2

January 3, 2009
geometrytrapezoidcircumcirclegeometry unsolved

Problem Statement

Let ABCD ABCD be an isosceles trapezium with AB∥CD AB \parallel{} CD and \bar{BC} \equal{} \bar{AD}. The parallel to AD AD through B B meets the perpendicular to AD AD through D D in point X. X. The line through A A drawn which is parallel to BD BD meets the perpendicular to BD BD through D D in point Y. Y. Prove that points C,X,D C,X,D and Y Y lie on a common circle.
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