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XC passes through the midpoint of the segment (16)

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October 29, 2010
trigonometrygeometry

Problem Statement

A circle touches the sides of an angle with vertex AA at points BB and C.C. A line passing through AA intersects this circle in points DD and E.E. A chord BXBX is parallel to DE.DE. Prove that XCXC passes through the midpoint of the segment DE.DE.