An example of this can be seen below. Once the tangent is found you can use it to find the gradient of the graph by using the following formula: \(\text{Gradient to the curve =}~\frac {y_2-y_1} ...

You are usually given the point - it's where the tangent meets the circle. To find the gradient use the fact that the tangent is perpendicular to the radius from the point it meets the circle.