Equidistant
![Perpendicular bisector of a line segment. All the points on the red line are equidistant from the two end points of the black line segment.](/Images/godic/202501/11/Perpendicular_bisector5151.gif")
![The cyclic polygon P is circumscribed by the circle C. The circumcentre O is equidistant to each point on the circle, and a fortiori to each vertex of the polygon.](/Images/godic/202501/11/Circumscribed_Polygon.svg5151.png")
A point is said to be equidistant from a set of objects if the distances between that point and each object in the set are equal.
In two-dimensional Euclidean geometry the locus of points equidistant from two given (different) points is their perpendicular bisector. In three dimensions, the locus of points equidistant from two given points is a plane, and generalising further, in n-dimensional space the locus of points equidistant from two points in n-space is an (n−1)-space.