# Length of the Tangent to a Circle

Let the tangent drawn from the point meet the circle at the point as shown in the given diagram. The equation is given by

Consider the triangle formed in this way is a right triangle, so according to the given diagram we have

It is observed that is the radius of the circle, so .

We also have

Putting all these values in (ii), we get

This gives the length of the tangent from the point to the circle .

Similarly, we can show that the is also of the same length.

**Example:** Find the length of the tangent from to the circle

Dividing the equation of the circle by **3**, we get the standard form

The required length of the tangent from is