# Thread: 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.
It asks for the radius, the value of r.

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!