The circle with center and radius touches externally the circle center radius . The tangent at their common point passes through the origin. Show that,

If also, the other two tangents from the origin to and are perpendicular, prove that .

Hence show that if remains fixed but and vary, then lies on the curve

.

I'm quite sure if I know how to do the first part, I should be able to do the rest, but I don't even know how to start. Thanks for any help.