Label the two angles in the diagram and . Then and theOriginally Posted by ParadiseIsle
slope of the common tangent is .
Now write in terms of .
Now write the equation of lines of slope through
, and (in terms of ). As these are two
ways of writing the equation of the common tangent equate the constant
terms and solve for , which will allow you to express the
common tangent in terms of what you know.
It may in practice be easiest to solve for numerically.