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I can find the equation of the tangent to a circle at any given point.

Muuji qoraalka
Using the gradient of the radius through a given point, you can find the equation of the tangent at this same point. You have already proved that the tangent at any point on a circle is perpendicular to the radius at that point. You have already proved that the product of the gradients of two perpendicular lines is -1 Using the gradient of the tangent and the coordinates of the point, you can find the equation of the tangent.

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