Question

The length of the tangent from an external point on a circle is ______ 

Options

• always greater than the radius of the circle.

• always less than the radius of the circle.

• may or may not be greater than the radius of the circle.

• None of these.

Answer 1

The length of the tangent from an external point on a circle is may or may not be greater than the radius of the circle.

Explanation: 

Observe the figure,

In the figure, OQ is the radius and QP is the tangent.

For the right triangle OQP, radius and tangents are two smaller sides, smaller than hypotenuse OP.

Also, the length of the tangent depends upon the distance of an external point from the circle. Thus,

The length of the tangent from an external point on a circle may or may not be greater than the radius of the circle.