Geometry · Similar triangles · Right triangles · Isosceles triangles · Altitudes · Pythagorean theorem
The triangle \(ABC\) has side lengths \(|AB| = 15\) cm, \(|BC| = 14\) cm and \(|CA| = 13\) cm. Let \(D\) be the foot of the altitude drawn from \(A\) to the side \(BC\), and let \(E\) be the point of that altitude for which \(\angle BAD = \angle DEC\). The lines \(AB\) and \(CE\) meet at \(F\). Determine \(|EF|\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2008, 1. letnik, category A, problem 3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source