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Problem in Plane Geometry

Published online by Cambridge University Press:  20 January 2009

M. Edouard Collignon
M. Edouard Collignon
Affiliation:
Inspecteur général des Ponts et Chaussées en retraite, Examinateur honoraire à l'Ecole polytechnique, Paris.
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In a plane, a point O and a straight line OH drawn through O are given. OH is the bisector of an unknown angle YOX, which it is required to determine by the following conditions:

A point I, given by position in the plane of the figure, is connected with the straight line OH by the given angle IOH =θ, and by the distance OI=c, from the point I to the vertex of the angle. This point I is the middle of a chord AB inscribed in the angle YOX, Furthermore the product OA × OB of the distances to the point O of the extremities of this chord is equal to a given quantity K2.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , February 1907 , pp. 2 - 9
Copyright
Copyright © Edinburgh Mathematical Society 1907