For a school investigation we had to use the co-ordinates from 3 towns and find out the point equidistant from all 3 for the location of a sports arena. I did all that, and now we have some extension tasks to work on.

I am having a bit of trouble on a couple.
1. Suggest a method for completing this exercise if a fourth town was included?

2. why do the perpendicular bisectors of a triangle always meet? Prove this using co-ordinate geometry.

Any help would be greatly appreciated, thanks!