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.

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The coordinates of the .

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

Slope of the line joining the points and :

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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 .

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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 .