Math problem: How to locate the tangent point of two circles that are separated from each other?

This can be said from the angle.

From your diagram, let the center of the great circle be a, the tangent point be c, the center of the small circle be b, and the tangent point be d.

If b is the vertical line of AC, and the vertical foot is E, AE = R-R.

Then the cosine of BAC is equal to AE/AB = (r-r)/q.

Then use the inverse triangle to calculate the degree of angle BAC.

So if you know the angle of BAC and the degree you calculate, it is the tangent point.

Or you know that the cosine of BAC is equal to the calculated (R-r)/Q, which also means that the point is a tangent point.