Hi, Teddo!
That's what happens to me as well. I briefly see the "hand" whenever I touch the circles, and then it quickly disappears and the circles go whichever way they choose. I *finally* got them inside the box above the words "Agia Sophia", but now discover that they have to be in a different location inside the box.
IMHO, it would be in the best interest of the game developers to have included a bypass for puzzles such as this, because if at least 3 of us here are stuck on the same puzzle, I'm betting there's a lot more out there.
I tried again last night for awhile, without success, so I'm about ready to give up.
Susan