Geometric locus of points equidistant from two given points.

The perpendicular bisector of a side of a triangle is a line that is perpendicular to a side of the triangle and that passes through its midpoint.

### Properties

- The three perpendicular bisectors of triangle ABC intersect at point O, which is the centre of the circle circumscribed about the triangle.

- The perpendicular bisector of a line segment is the line that is perpendicular to the line segment and that passes through its midpoint. The line
*d*is the perpendicular bisector of segment AB.

Therefore :*d*(P\(_i\), A) =*d*(P\(_i\), B) and point O is the midpoint of segment AB.