Geometry · Ruler and compass construction · Circumcircle · Inscribed angles · Arc of a given angle · Equilateral triangle
Problem 2, 2000
An acute triangle \(ABC\) is given. Construct, with ruler and compass, a point \(P\) inside the triangle such that the rays \(AP\), \(BP\) and \(CP\) meet the circumcircle of \(ABC\) again in the three vertices of an equilateral triangle.
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Serbian Republic Competition (Republicko takmicenje) 2000, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source