This problem is ill defined

This problem is ill defined. Insted of putting the tiles such that the center of the circle is at the intesection of tiles one could put the tiles such that the center of the central tile lies at the center of the circle.

For a radius of 2.49999 one would get 9 solid and 16 partial tiles intead of 12 and 20.

So you might want to put that constraint in the problem description.