Geometry · Similar triangles · Quadrilateral · Angle chasing · Spiral similarity
Let \(ABCD\) be a quadrilateral and let \(K\) be a point inside triangle \(ABD\) such that triangles \(ABD\) and \(KCD\) are similar, the vertices corresponding in the written order. Prove that triangles \(BCD\) and \(AKD\) are then similar as well.
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2008, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source