Re: I ask mathematicians for help

On 2025-05-13 11:48:13 +0000, Luigi Fortunati said:

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

First you must check that the circles A and B don't touch. Otherwise
P cannot be between them.

The point P divides the line segment between the centres of A and B in
the ratio of the radii of A and B; i.e,

(distance from the center of A to P) = (radius of A) * (distance from
the centre of A to the centre of B) / (radius of B).

--
Mikko