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FB is perpendicular to AC when FD is perpenduclar to BC

Source: Baltic Way 2002

November 13, 2010
geometrycircumcircleparallelogramgeometry proposed

Problem Statement

Let ABCABC be an acute triangle with ∠BAC>∠BCA\angle BAC>\angle BCA, and let DD be a point on side ACAC such that ∣AB∣=∣BD∣|AB|=|BD|. Furthermore, let FF be a point on the circumcircle of triangle ABCABC such that line FDFD is perpendicular to side BCBC and points F,BF,B lie on different sides of line ACAC. Prove that line FBFB is perpendicular to side ACAC .
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