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equilateral triangles and parallelogram

Source: Romanian TST 5 2007, Problem 1

June 7, 2007
geometryparallelogramgeometric transformationrotationreflectionanalytic geometryperpendicular bisector

Problem Statement

Let ABCD ABCD be a parallelogram with no angle equal to 60o 60^{\textrm{o}}. Find all pairs of points E,F E, F, in the plane of ABCD ABCD, such that triangles AEB AEB and BFC BFC are isosceles, of basis AB AB, respectively BC BC, and triangle DEF DEF is equilateral.
Valentin Vornicu
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