Area of a sector
\(\Gamma\) is a circle with center \(O\). \(A\) and \(B\) are points on \(\Gamma\) such that the sector \(AOB\) has a perimeter of \(40\). Amongst all circular sectors with a perimeter of \(40\), what is the central measure of \(\angle AOB\) (in radians) of the sector with the largest area?
Details and assumptions
A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle.