Parametric Math Problem ...

Trying to calc out the xy locations for two tangent arcs...see link for
details.
Any help would be appreciated.

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Need for a parametric program for a CNC router. I have it figured out on one
of our other CNC routers (A Weeke Venture 5L via WoodWOP) but on our Busellato
routers I can't program it the same way parametrically with a fillet. I've
actually contacted the machine manufacturer and they said I'd need to trig it
out to achieve this. And I've been racking my head for a while.