I am trying to draw the profile of the tyre of a railway vehicle. In essence it consists of three circles in contact. The size and position of the two smaller circles are fixed. The position of the larger circle (but not the size) needs to be adjusted so that it makes glancing contact with the two smaller circles. The contact must be such that the excess parts of all three circles can be trimmed away.
I expect there is some easy way of getting the circles to connect at the contact points, but I can't find it! Help please.
Drawing of three circles is attached.