Let $PQ$ be a line segment and $A$ a point not belonging to $PQ$ . Let the magnitude of the angle $PAQ$ be $\alpha$ . One says that the line segment $PQ$ is seen from the point $A$ in an angle of $\alpha$ ; one may also speak of the angle of view of $PQ$ .

The locus of the points from which a given line segment $PQ$ is seen in an angle of $\alpha$ (with $0 < \alpha < 180^\circ$ ) consists of two congruent circular arcs having the line segment as the common chord and containing the circumferential angles equal to $\alpha$ .

Especially, the locus of the points from which the line segment is seen in an angle of $90^\circ$ is the circle having the line segment as its diameter.

Note. The explementary arcs of the above mentioned two arcs form the locus of the points from which the segment $PQ$ is seen in the angle $180^\circ\!-\!\alpha$ .