The centre of the required circle is at a distance ofOriginally Posted by Helder Barros
from , and also at a distance of from .
Hence the centre is at the point of intersection of:
(note there can be zero one or two solutions to this, also this
is for exterior tangency, if is large enough we
can also have interior tangency which would require a change to
the RHS of the equations to and respectivly.
Now I think of it you can also have mixed interior
and exterior tangency)