you cannot do this on the plane. try proving this yourself. but a regular tetrahedron in space for example is an example where there four points equidistant from each other.
For three points, (x1,y1), (x2,y2) & (x3,y3), you can set up 3 distance equations with variables x, y & z:
z^2 = (x-x1)^2 + (y-y1)^2
z^2 = (x-x2)^2 + (y-y2)^2
z^2 = (x-x3)^2 + (y-y3)^2
3...
-- Draw a line segment from one point to the other. -- Construct the perpendicular bisector of the line segment.. -- Every point on the perpendicular bisector of the line segment is equidistant from...