Nerd up! Geometry time suckage within

Stuck on level 20. I even broke down and looked at some of the posted answers after I was convinced I had gotten it right and it was just a bug. I couldn't really figure out why mine didn't register, as the intersections showed one point on each circle, unless there was some overlap I couldn't see and it wasn't exact.

Anyways, I still can't figure out why those answers for 20 work, and I'll be busy with graph paper and drafting tools 'til I figure it out. Darn this game!