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Show that EF bisects angle CFD

Source: IMO Shortlist 1994, G1

October 22, 2005
trigonometrygeometrysymmetryangle bisectorIMO Shortlist

Problem Statement

C C and D D are points on a semicircle. The tangent at C C meets the extended diameter of the semicircle at B B, and the tangent at D D meets it at A A, so that A A and B B are on opposite sides of the center. The lines AC AC and BD BD meet at E E. F F is the foot of the perpendicular from E E to AB AB. Show that EF EF bisects angle CFD CFD
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