Problem in Plane Geometry

Abstract

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 K 2 .