I am writing some code to participate in an AI challenge. The main objective of the AI challenge is to take a simulated robot and navigate it through a maze to a destination zone. The secondary objective which is optional is to find a recharger placed in the maze at an unknown location. This is all done in a 2D grid.

My program can call a method to get a distance measurement from the recharger. So using trilateration I should be able to locate the recharger by calling this method, recording my ai's current position and the distance the recharger is away from that point 3 times over.

I found this example of trilateration on Wikipedia __http://en.wikipedia.org/wiki/Trilateration__ but this applies to a 3d space. I'm only dealing with a 2D space. Also, I don't understand how to use the formula shown in Wikipedia, searching the web for a working example with numbers plugged in and boiling down to the final coordinates is scarce with Google searches.

I'm not a math major; I am just an enthusiast exploring AI problems.

An explanation and step by step example of how to calculate the problem are what I need as mathematics is not my strong point. Below is some sample data:

Point 1: x=39, y=28, distance=8

Point 2: x=13, y=39, distance=11

Point 3: x=16, y=40, distance=8

Any example using my sample data would be greatly appreciated. The programming to this will be very straight forward once I can wrap my head around the mathematics.