# Locus of points a fixed distance from a given point

Martin McBride

2020-08-22

The locus of all points that are a fixed distance *r* from a given point *P* is a circle. The circle has a radius *r* and has its centre at *P*.

In this animation, the blue dot represents *P*, and the grey line represents the distance *r*. The circle is formed as the red dot moves through all the points in the locus, tracing out the circle:

## Points that are less than a fixed distance from a given point

The points that are less than a fixed distance *r* from the point *P* are all the points that fall inside the circle. This is illustrated below:

This topic is also covered by this video: