To find the equation of a circle when you know the radius and centre, use the formula \({(x - a)^2} + {(y - b)^2} = {r^2}\), where \((a,b)\) represents the centre of the circle, and \(r\) is the ...

A model of the famous toy known as a spirograph. A circle of radius r (see blue circle below) is allowed to roll around the inside of a circle of radius R (see black circle below). We assume that the ...

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.