Equidistant line from two fixed points

Each point P in turn on the red line is equidistant from points X and Y.

The red line represents the locus of points equidistant from X and Y.

Equidistant line from a fixed point (a circle)

All the points P lie on a locus of points the same distance from O.

(i.e on the perimeter of the circle)

Equidistant line from two lines joined at a vertex

Each point P in turn on the red line is equidistant from lines OX and OY.

The red line represents the locus of points equidistant from lines OX and OY.

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