A tangent to a circle at point P is a straight line that touches the circle at P. The tangent is perpendicular to the radius which joins the centre of the circle to the point P.

The radius that joins the centre of the circle (0, 0) to the point P is at right angles to the tangent, so the gradient of the tangent is the negative reciprocal of the gradient of the radius.

Where Pi (π) is of course the number and r is the radius of the circle. Where does this formula come from? One method of obtaining this equation is to integrate dxdy over the area of a circle ...