A fur dresser had to put a patch shaped like a scalene triangle on a piece of fur. Suddenly he realized he had made a terrible mistake. The patch fitted the hole but the fur side faced the wrong way.
The fur dresser, after some thought, cut the triangular patch into 3 parts, each of which would be unchanged when turned over. How?
(In reply to re(2): Half an answer
Nope, the circumcenter is the only point equidistant from all vertices. Note, however, that Victor didn't specify that the parts had to be triangles.