criteria to find a point equidistant from given n points Is there any procedure to find a point equidistant from given $n$ number of points $(n\gt2)$. Our prior assumption is that they may not form a regular polygon. Please suggest a method, that could be of any type geometric,or numerical method. 
Thanks in advance
 A: Being equally distant from two points means being situated on the perpendicular bisector of the segment determined by those two points. Now, in the case of three points, we have two straight lines $($the perpendicular bisectors of each segment$)$, which obviously intersect in one point only,if the three points are not collinear $($and in none if they are collinear, since the two perpendicular bisectors will in that case be parallel to one another$)$. And we know from middle-school that the perpendicular bisector of the third segment will also pass through that same point of intersection, since in a triangle the perpendicular bisectors are concurrent. Now, if the perpendicular bisector of any segment created by the addition of a fourth point will not pass through that same point, then there is no point of intersection of all perpendicular bisectors, and hence no point equally distant from all other points. Which is basically the same as what Jack already said in far fewer words in his very short and concise comment.
