You can draw another circle inside the first having a diameter that is (√2)/2 times the diameter of the first. The circle you drew will cut the original area in half.

You can draw any of a number of geometric shapes inside the circle to cut the area in half. If you want to cut the perimeter of your circle in half, only a diameter will do.

You can draw any of a number of geometric shapes inside the circle to cut the area in half. If you want to cut the perimeter of your circle in half, only a diameter will do.