hii

 

see the question in terms of normal goemetry .. the the point such that it is equi-distant from the two points lie on the perpendicular bisector ..

 

Now we want that point to be equidistant from the other (third) point also .. so there is a simple thing that there can be only such point and that point will be the circumcenter of the triangle formed by three points ..

 

I hope this is clear ..

 

cheers