Monge's problem asks one to draw a circle that cuts three given circles perpendicularly.
The solution is known as the radical circle of
the given three circles. If it lies outside the three
circles, then the circle with
center 
and radius formed by the tangent from 
to one of the given circles intersects the given circles
perpendicularly. Otherwise, if 
lies inside one of the circles, the problem is unsolvable.
