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  ) 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