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equal angles in an isosceles trapezoid of perpendicular diagonals

Source: 2015 Sharygin Geometry Olympiad Correspondence Round P8

August 2, 2018
geometrytrapezoidisoscelesperpendicularequal angles

Problem Statement

Diagonals of an isosceles trapezoid ABCDABCD with bases BCBC and ADAD are perpendicular. Let DEDE be the perpendicular from DD to ABAB, and let CFCF be the perpendicular from CC to DEDE. Prove that angle DBFDBF is equal to half of angle FCDFCD.
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