According to the equation of a circle, find the derivative y' of y about x (there are two values, think about why there are two), and then calculate the derivative of y* of another circle. Suppose there is a situation where y*' is equal to y', calculate X, and then substitute it into the equations of two circles to find their respective Y. If two Y's are equal, they are tangent.

According to this method, we can also find out whether the ellipse is tangent.

If you want to know whether it is tangent or tangent, you can calculate it by the second derivative of two circles, and then judge whether the two second derivatives are of the same sign.