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angle of view of a line segment
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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 $180^\circ\!-\!\alpha$ .
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"angle of view of a line segment" is owned by pahio.
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Cross-references: segment, explementary arcs, diameter, circle, circumferential angles, chord, arcs, circular, congruent, locus, angle, point, line segment
There are 3 references to this entry.
This is version 9 of angle of view of a line segment, born on 2007-10-04, modified 2007-10-14.
Object id is 9980, canonical name is AngleOfViewOfALineSegment.
Accessed 2252 times total.
Classification:
| AMS MSC: | 51F20 (Geometry :: Metric geometry :: Congruence and orthogonality) | | | 51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries) |
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Pending Errata and Addenda
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