Locuses of points on a plane

The locus of points on a plane is the set of all points on the plane that satisfy some given condition. From this definition it follows that there are no other points on the plane that satisfy this condition.

Locus of points equidistant from one point

1. The locus of points equidistant from one point is a circle with center at that point.
2. The locus of points equidistant from the sides of an angle and lying inside the angle is the angle bisector.

Locus of points equidistant from the ends of a segment

3. The locus of points equidistant from the ends of the segment is the median perpendicular.

Locus of points equidistant from a given line

4. The locus of points located at a distance d from a given line is a pair of parallel lines.

The locus of points from which a given segment is visible at a given angle

5. The locus of points from which a given segment is visible at a given angle is two arcs (excluding their end points) of two circles of the same radius for which the given segment is a common chord.

Locus of midpoints of chords of a circle, drawn from one point of this circle.

6. The locus of the midpoints of the chords of a given circle drawn from one point of this circle is a circle of half the radius passing through this point and the center of the given circle.