# Spheres Touching

• Sep 28th 2011, 09:27 AM
Bracketology
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?
• Sep 28th 2011, 09:36 AM
Plato
Re: Spheres Touching
Quote:

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 \$\displaystyle (0,0,0)~\&~(4,3,12)\$
• Sep 28th 2011, 09:43 AM
Bracketology
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?
• Sep 28th 2011, 09:52 AM
Plato
Re: Spheres Touching
Quote:

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 \$\displaystyle (0,0,0)~\&~(4,3,12)\$
• Sep 28th 2011, 09:53 AM
Bracketology
Re: Spheres Touching
Oh yea. That makes sense. Thanks!