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Line joining circumcentres is perpendicular to FC

Source: Baltic Way 1997

January 28, 2011
geometry proposedgeometry

Problem Statement

Five distinct points A,B,C,DA,B,C,D and EE lie on a line with ∣AB∣=∣BC∣=∣CD∣=∣DE∣|AB|=|BC|=|CD|=|DE|. The point FF lies outside the line. Let GG be the circumcentre of the triangle ADFADF and HH the circumcentre of the triangle BEFBEF. Show that the lines GHGH and FCFC are perpendicular.
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