Question

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

Answer 1

PT is a tangent drawn from an external point P on the circle with centre O.

∠OTP = 90º (Radius is perpendicular to the tangent at the point of contact)

So, ∆OPT is a right triangle. OP is the hypotenuse of the right ∆OPT.

∴ OP > PT (In a right triangle, hypotenuse is the longest side.)

Or PT < OP

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

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