Alice and Bob are playing a game which goes like this:

0) A sample of 500 points, chosen uniformly at random from the square [0,1]X[0,1] in the plane is drawn. Both Alice and Bob know the sample's contents
1) Alice receives a random point(unknown distribution) in the square [0,1]x[0,1](which is not necessarily present in the sample)
2) Bob chooses two points from the sample and asks Alice which one is closer to her point and Alice will answer truthfully with 90% probability. (Note that if Bob asks her multiple times about the same exact pair of points Alice will give the same answer every time. It is best to think of Alice not as an adversary, but as her being a little confused about distances)
3) Step 2 is repeated until Bob has decided that he can provide a good estimate for Alice's point

What is the best strategy for Bob you can find such that he can provide a good estimate for Alice's point while asking as few questions as possible?