Geometry · Reflections · Angles between lines · Concurrent lines · Isometries
The lines containing the two diagonals of a quadrilateral \(ABCD\) meet at an angle of \(60^{\circ}\). Each vertex of the quadrilateral is reflected in the line containing the diagonal that joins its two neighbouring vertices: thus \(A\) and \(C\) are reflected in the line \(BD\), while \(B\) and \(D\) are reflected in the line \(AC\). Prove that the four image points lie on one line.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2017, 1. letnik, category A, problem B2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source