Geometry · Angle bisector · Isosceles triangle · Similar triangles · Geometric mean
In a triangle \(ABC\), the bisector of the angle \(\angle BAC\) meets the side \(BC\) at the point \(D\). The triangle \(ADC\) is isosceles with apex \(D\), that is, \(|DA| = |DC|\). Given \(|CD| = 36\) and \(|BD| = 64\), find the lengths of the sides of the triangle \(ABC\).
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), regijsko (regional) round 2011, 1. letnik, category A, problem B2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source