Geometry · Isosceles triangle · Angle inequality · Perpendicular distance
In a triangle \(ABC\) the angle at \(B\) is obtuse, \(\angle ABC > 90^\circ\), and the side \(AC\) is twice as long as \(AB\), that is \(2\cdot AB = AC\). Prove that
\[ 2\cdot\angle ACB > \angle BAC. \]
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Serbian Municipal Competition 2012, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source