# Area of a sector

Geometry Level pending

$$\Gamma$$ 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.

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