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Extrema for a function defined on a square

Source: Greek national M.O. 1997, Final Round, problem 1

November 20, 2011
functiongeometry unsolvedgeometry

Problem Statement

Let PP be a point inside or on the boundary of a square ABCDABCD. Find the minimum and maximum values of f(P)=∠ABP+∠BCP+∠CDP+∠DAPf(P ) = \angle ABP + \angle BCP + \angle CDP + \angle DAP.
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