Question

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

Options

• always greater than OP

• equal to OP

• always less than OP

• information insufficient

Answer 1

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

Explanation:

Observe figure

The angle between tangent and radius is 90º. This implies OP is the hypotenuse for the right triangle OQP right-angled at Q and hypotenuse is the longest side in a right triangle, therefore the length of the tangent from an external point P on a circle with centre O is always less than OP.