Question

The length of the tangent from an external point P on the circle with centre O is always ______ OP.

Answer 1

The length of the tangent from an external point P on the circle with centre O is always less than OP.

Explanation:

Let PT be the tangent from external point P to the circle with centre O, and let OT = r (point of contact T).

Since the radius OT is perpendicular to the tangent PT, triangle OTP is right-angled, so by Pythagoras OP² = OT² + PT². 

Therefore PT² = OP² – OT² < OP². 

Hence PT < OP.