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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 ...
The set of points equidistant from two points is a perpendicular bisector to the line segment connecting the two points. [8] The set of points equidistant from two intersecting lines is the union of their two angle bisectors. All conic sections are loci: [9] Circle: the set of points at constant distance (the radius) from a fixed point (the ...
In mathematics, an equidistant set (also called a midset, or a bisector) is a set whose elements have the same distance (measured using some appropriate distance function) from two or more sets. The equidistant set of two singleton sets in the Euclidean plane is the perpendicular bisector of the segment joining the two sets. The conic sections ...
The locus of points equidistant from two given points is a straight line that is called the perpendicular bisector of the line segment connecting the points. The perpendicular bisectors of any two sides of a triangle intersect in exactly one point. This point must be equidistant from the vertices of the triangle.
In geometry, a centre (British English) or center (American English) (from Ancient Greek κέντρον (kéntron) 'pointy object') of an object is a point in some sense in the middle of the object. According to the specific definition of centre taken into consideration, an object might have no centre.
In 4-dimensional Euclidean space, it is the set of points equidistant from a fixed central point. The interior of a 3-sphere is a 4-ball . It is called a 3-sphere because topologically, the surface itself is 3-dimensional, even though it is curved into the 4th dimension.
Annulus: a ring-shaped object, the region bounded by two concentric circles. Arc: any connected part of a circle. Specifying two end points of an arc and a centre allows for two arcs that together make up a full circle. Centre: the point equidistant from all points on the circle.
In hyperbolic geometry, a hypercycle, hypercircle or equidistant curve is a curve whose points have the same orthogonal distance from a given straight line (its axis). Given a straight line L and a point P not on L , one can construct a hypercycle by taking all points Q on the same side of L as P , with perpendicular distance to L equal to that ...