Take O as the origin, let the radii of the two circles be R and R', and let the lines joining their centres to O make angles α and α' with the initial line.
The equations to the two circles are therefore,
From (1) the locus of S is a circle, whose radius is R", which passes through the origin O and is such that the line joining O to its centre is inclined at an angle a" to the initial line.
