# angle of view of a line segment

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 $180^{\circ}\!-\!\alpha$.

 Title angle of view of a line segment Canonical name AngleOfViewOfALineSegment Date of creation 2013-03-22 17:34:11 Last modified on 2013-03-22 17:34:11 Owner pahio (2872) Last modified by pahio (2872) Numerical id 14 Author pahio (2872) Entry type Topic Classification msc 51M04 Classification msc 51F20 Related topic CircumferentialAngleIsHalfCorrespondingCentralAngle Related topic ThalesTheorem Related topic CalculatingTheSolidAngleOfDisc Related topic ExampleOfCalculusOfVariations Related topic ProjectionOfRightAngle Defines angle of view