A circle of radius 2 has a circular hole of radius 1.

This is done is two alternative ways: in one the hole is tangent to the larger circle forming a crescent shape; in the other the hole is in the exact centre of the larger hole.

In the ‘crescent’ option a shaded circle of radius 1 is drawn, and then infinitely many smaller and smaller shaded circles are added heading off towards the two tips of the crescent.

In the ‘ring’ option just nine circles, each of radius ½ are drawn and shaded.

Which version has the largest combined shaded area?