Geometry · Triangle construction · Isosceles triangles · Exterior angle theorem · Triangle inequality
Two segments of lengths \(a\) and \(b\) are given. Construct a triangle \(ABC\) having these two segments as sides, in such a way that the angle opposite one of them is three times as large as the angle opposite the other.
Carry out the construction, prove that the triangle it produces has the required property, and determine for which \(a\) and \(b\) the construction is possible.
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Serbian Regional Competition 2014, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source