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trapezium inscribed in circle, silk road

Source: SRMC 2012

September 2, 2018
geometrytrapezoidcircumcircle

Problem Statement

Trapezium ABCDABCD, where BC∣∣ADBC||AD, is inscribed in a circle, EE is midpoint of the arc ADAD of this circle not containing point CC . Let FF be the foot of the perpendicular drawn from EE on the line tangent to the circle at the point CC . Prove that BC=2CFBC=2CF.
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