Acell phone company is looking to place a new tower to service 3 cities. in order for it to best service each city, it needs to be equidistant from all 3 cities. what mathematical concept could they use to find a location that is equidistant from all 3 cities? why is this a good method?

A circle is a collection of points all of which are on the circumference of the circle.  If you use algebra and (x-h)^2 + (y-k)^2 = r^2 and the info contained in the coordinates (x,y) of each city, you can find h, k and r.  Then r is the (equal) distance between each city and the center of the circle, where the new tower will be built.