Problem

Source: Romanian TST 5 2007, Problem 1

Tags: geometry, parallelogram, geometric transformation, rotation, reflection, analytic geometry, perpendicular bisector



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