I ask mathematicians for help

In the animation https://www.geogebra.org/classic/dcphg8s2 there are two lines that pass through point P and are tangent to both sphere A and sphere B.

However, if I change the dimensions of sphere B with the appropriate slider, the two lines continue to be tangent to sphere B but no longer to sphere A.

To ensure that the two lines are also tangent to sphere A, I have to manually change the position of point P on the x-axis (taking it and moving it with the mouse).

I would like to make this movement of P automatic (at each change of sphere B) to keep the new lines always tangent to sphere A.

With what formula can I do this, knowing the dimensions of spheres A and B and their distance?

Luigi Fortunati