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Show that points P,Q,X, Y lie on a circle

Source: Austrian Mathematical Olympiad 2000, Part 2, D1, P2

June 28, 2011
geometrytrapezoidgeometry proposed

Problem Statement

A trapezoid ABCDABCD with AB∥CDAB \parallel CD is inscribed in a circle kk. Points PP and QQ are chose on the arc ADCBADCB in the order A−P−Q−BA-P -Q-B. Lines CPCP and AQAQ meet at XX, and lines BPBP and DQDQ meet at YY. Show that points P,Q,X,YP,Q,X, Y lie on a circle.
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