Construction of a chord meeting two conditions: 1) It passes through a given point inside the circle. 2) It is inscribed in an arc equal to a given angle.
Notes: There is not always a solution. Chords inscribed in arcs of equal length are the same distance from the origin. If A lies inside the circle with radius OP, no intersection is possible. More about finding the tangents to a circle: [i]http://www.geogebratube.org/material/show/id/30749[/i]