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Quadrilateral BECD and triangle ABC have the same area

Source: Germany Bundeswettbewerb Mathematik 2001, Round 1, Problem 3

February 1, 2009
geometrycircumcircleparallelogramtrigonometrygeometry unsolved

Problem Statement

Let ABC ABC an acute triangle with circumcircle center O. O. The line (BO) (BO) intersects the circumcircle again in D, D, and the extension of the altitude from A A intersects the circle in E. E. Prove that the quadrilateral BECD BECD and the triangle ABC ABC have the same area.
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