[yossi_peti]

Theoretically, if you choose the first two points at random, then you have a 50-50 chance of guessing right on the third guess (the two circles from the first two guesses have at most two intersecting points) and should always get the correct answer on the 4th guess.

[ke88y]

You can make up your own scoring system based upon the first two distances, with a high penalty (negative points) for needing the 4th guess.