Geometry · Isosceles triangles · Angle chasing · Foot of a perpendicular · Midpoints · Similar triangles
In triangle \(ABC\) the side \(AB\) is twice as long as \(AC\), that is \(|AB| = 2|AC|\). The point \(D\) lies on the ray \(CA\) and satisfies \(|CD| = 3|AC|\). Prove that the perpendicular dropped from \(C\) to the line \(BD\) bisects the segment \(AB\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2016, 1. letnik, category A, problem B2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source