# Math Help - Spheres Touching

1. ## Spheres Touching

The problem states:

A sphere centered at (4,3,12) is being inflated so that r increases from 0 to infinity. At some moment the sphere touches another sphere having an equation x^2+y^2+z^2=9, for the first time. What is the radius at this point?

I drew the picture and know that that equation makes a sphere with radius 3. How do I solve for the point where they touch?

2. ## Re: Spheres Touching

Originally Posted by Bracketology
The problem states:

A sphere centered at (4,3,12) is being inflated so that r increases from 0 to infinity. At some moment the sphere touches another sphere having an equation x^2+y^2+z^2=9, for the first time. What is the radius at this point?
I drew the picture and know that that equation makes a sphere with radius 3. How do I solve for the point where they touch?
Note that the question does not ask for the point.

However, the point is on the line segment with endpoints $(0,0,0)~\&~(4,3,12)$

3. ## Re: Spheres Touching

So would the radius be the distance from the point 4,3,12 to what? I would still need to know the point that they touch to find the radius?

4. ## Re: Spheres Touching

Originally Posted by Bracketology
So would the radius be the distance from the point 4,3,12 to what? I would still need to know the point that they touch to find the radius?
No you do not. At that point the sum of two radii is the distance between $(0,0,0)~\&~(4,3,12)$

5. ## Re: Spheres Touching

Oh yea. That makes sense. Thanks!