# The equation of tangent to the circle x^2+y^2=r^2 is y=mx+c ,then the point of contact of the circle and the tangent is?

##### 2 Answers

See below.

#### Explanation:

The point of contact can be found by equating the equations together. This will find a value that is common to both equations and consequently will be the point or points of contact.

So we have

rearranging:

Tangent line:

Point of contact:

where,

#### Explanation:

Let, the **Line** **Circle**

Clearly, **Centre** and **Radius** of

From **Geometry,** we know that, in a **circle,** the

the **centre** to a **tgt.** equals the **radius.**

Recall that, the

Utilising these facts, we have,

Hence, the tgt.

If **pt. of contact,** from **Geometry,** we know that,

So,

To find the eqn. of

its slope is

Solving

Therefore, the pt. of contact is,

**Enjoy Maths.!**