Better I add a pic:

http://pic-hoster.net/code/af0e139a00fff39403ed36b97bcabf36.gif
So, we can immediately ask for several natural possible loci:

1. Green areas equal (fiendish)

2. Yellow areas equal (trivial, incenter)

3. Arcs DE=FG=HI (middle difficulty, I give it a try)

4. Arcs EF=GH=ID (same as 2)

5. Triangle aress ADE=BFG=CHI (straight lines DE,FG,HI

have been omitted for clarity - middle difficulty)

Obviously, these can be used to combine two loci into

a point, but only 3+5 makes good sense. One solution

surely is the circumcenter, others might exist.

(Pic approximates case 3)

Hauke