Geometry · Extremal configuration · Convex position · Angle sum
Let \(A\), \(B\), \(C\), \(D\) be four points in the plane, no three of them collinear. Every choice of three of these points forms a triangle, so the four points determine \(12\) angles in all. Write \(f(A,B,C,D)\) for the measure of the largest of these \(12\) angles.
Determine
\[ \min f(A,B,C,D), \]
where the minimum is taken over all such quadruples of points.
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Serbian Municipal Competition 2017, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source