# 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 |