Filleting two circles

Hello,

I'd like to calculate the center co-ords (x,y)'s of the two possible circles given a radius, that satisfy the tangency requirement to two other circles of differing radii.  The latter two also are tangent to each other.  The end result should be that all four should be just touching each other.

The real world problem is for generating a fillet weld on each side of two rods of differing diameters touching each other.  Anybody who can help?  The problem is akin to but not exactly like the one shown here - http://rosettacode.org/wiki/Problem_of_Apollonius

Thank,

JMB

Hello,

Never mind!  I was needlessly making things complicated.  The easy way is to create two larger circles concentric with the two given rod diameters.  Each of these larger circles was larger in radius by a value equal to the radius of the weld fillet.  Then the intersection of these two larger circles become the center points of the weld fillet arcs.  Hope this helps others too!

Regards, JMB