تطبيق هندسي لمبدأ القيمة القصوى

In this paper we apply the Extremum Principle of Ioffe – Tichomirov to find the conditions that are satisfied by points of polygon ( with n sides ) inscribed in a given circle in order that the sum of the squares of these sides has the maximal value. It has been shown –as a special case - that the sum of the squares of quadrilateral (n=4) has the maximal value when one of its diameters coincides with diameter of the circle .