To do this, you need to work out the radius and the centre of each circle ... or the difference between their radii. Two circles will intersect at two points when \({r_1} ...

The radius of the ith circle is , where q is a quantile used to scale the ... If their circles are nested or nearly overlap so that the external angle of intersection is greater than 90 degrees, then ...

To work out the area of a circle: Find the value of the radius. If the diameter is given, this must be halved. Substitute the value of the radius into the formula for the area of a circle.