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Collinearity in Isosceles Trapezoid

Source: All Russian Olympiad 2017 Grade 9 Problem 2

July 5, 2017
geometrytrapezoidtangent

Problem Statement

ABCDABCD is an isosceles trapezoid with BC∣∣ADBC || AD. A circle ω\omega passing through BB and CC intersects the side ABAB and the diagonal BDBD at points XX and YY respectively. Tangent to ω\omega at CC intersects the line ADAD at ZZ. Prove that the points XX, YY, and ZZ are collinear.
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