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From: Luigi Fortunati <fortunati.luigi@gmail.com>
Newsgroups: sci.physics.research
Subject: Re: I ask mathematicians for help
Date: 15 May 2025 10:49:35 GMT
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Mikko il 14/05/2025 18:12:02 ha scritto:
>> 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).

Ok but in the denominator there must be the sum of the radii (radius of 
A + radius of B).

I changed the coordinates of the point P of my animation and you can 
see that it works perfectly.

Thanks for the answer.

Luigi.