Assume the center of the circle  as .

The equation of the circle with radius  is .

Consider the point on the circle .

So the  satisfy the equation of the circle.

.

The coordinates of the .

Slope of the line joining two points  and  is given by .

Slope of the line joining the points  and :

.

Slope of the radius  is .

Equation of the circle is .

Slope of the tangent is derivative of the function at a particular point.

Find the derivative of the circle equation.

Consider .

Differentiate on each side with respect to . 

Slope of the tangent line at  is .

Slope of the tangent is .

If the two lines with slopes  and  are perpendicular to each other , then .

Consider slope of the radius  as  and Slope of the tangent as .

Determine the product of the slopes of  line and tangent line at .

.

Hence it is said to be that slope of the tangent at  is perpendicular to the radius .

Slope of the tangent at  is perpendicular to the radius .