Question

From an external point P, two tangents PA and PB are drawn to the circle with centre O. Then the angle between OP and AB is ______.

Answer 1

From an external point P, two tangents PA and PB are drawn to the circle with centre O. Then the angle between OP and AB is 90°.

Explanation:

Let AB be the chord of contact and let OP meet AB at M. Since PA and PB are tangents, OA ⟂ PA and OB ⟂ PB, so triangles OAP and OBP are right and congruent (OA = OB, OP common). Hence OP bisects ∠AOB and therefore passes through the midpoint of chord AB and is perpendicular to AB. Thus the angle between OP and AB is 90°.