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isosceles trapezoid inscribed an isosceles trapezoid, equal products wanted

Source: Sharygin Final 2007 9.2

April 30, 2019
geometrytrapezoidisosceles

Problem Statement

Points EE and FF are chosen on the base side ADAD and the lateral side ABAB of an isosceles trapezoid ABCDABCD, respectively. Quadrilateral CDEFCDEF is an isosceles trapezoid as well. Prove that AE⋅ED=AF⋅FBAE \cdot ED = AF \cdot FB.
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