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Show that two angles are equal

Source: Junior Turkish Mathematical Olympiad 2010 Problem 1

July 24, 2011
geometryrectangleratiocircumcirclepower of a pointgeometry proposed

Problem Statement

A circle that passes through the vertex AA of a rectangle ABCDABCD intersects the side ABAB at a second point EE different from B.B. A line passing through BB is tangent to this circle at a point T,T, and the circle with center BB and passing through TT intersects the side BCBC at the point F.F. Show that if ∠CDF=∠BFE,\angle CDF= \angle BFE, then ∠EDF=∠CDF.\angle EDF=\angle CDF.
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