From Newsgroup: sci.physics.research

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
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From Newsgroup: sci.physics.research

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
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From Newsgroup: sci.physics.research

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.
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From Newsgroup: sci.physics.research

On 2025-05-15 10:49:35 +0000, Luigi Fortunati said:

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).

You are right about that.

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

Thanks for the answer.

You are welcome.
--
Mikko
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