Question

Prove that the locus of the point whose chord of contact with respect to a circle subtends a right angle at the centre of the circle is its director circle.

Answer 1

P is a point and AB its chord of contact with respect to a circle with centre C (see Fig.) such that  ΔBCA = 90°. Since CA and CB are at right angles to the tangents PA and PB, respectively. It follows that  ΔAPB is a right-angled triangle. Hence, point P lies on the director circle of the given circle.