Touching Circles or spheres problem

[rpmwebs]

Is there an equation that could calculate the distance between the centre of two different sized circles (or spheres when they touch on a flat surface. (i.e. Assume two different sized marbles on a flat surface touch, what would be the distance between the two centre points if they were dropped perpendiclar onto the surface)

as one marble gets smaller it gets closer to the other

 

[rpmwebs]

solved it

I have just sat down with some scrap paper and I think I may have solved it.

if R1 is the radius of the large circle and R2 is the radius of the small, and x is the distance I am trying to find then:

x = ( sqrt of (R1 + R2)) - (R2 - R1)^2

my notation is a little poor but it was much easier than I thought it would be.

Any alternative solutions would be welcome

PM

 

[Deleted member 4993]

Is there an equation that could calculate the distance between the centre of two different sized circles (or spheres when they touch on a flat surface. (i.e. Assume two different sized marbles on a flat surface touch, what would be the distance between the two centre points if they were dropped perpendiclar onto the surface)

as one marble gets smaller it gets closer to the other

There is a theorem:

If two circles touch each other (tangent) then the centers and the tangent are on a straight line.

Use that knowledge.....

 

[rpmwebs]

Why don't you draw the 2 circles,
then draw a line joining the centers:
answer will be apparent...and SIMPLE....

You have not understood my question.

Imagine two different sized marbles on a flat table. If they are rolled together until they touch the distance between the centres of the spheres (if the centres of each sphere are dropped perpendicular to the table surface and then measured at the table plane) would be less than the sum of the two radii (unless the spheres were the same size)

anyway I solved the problem shortly after posting but thank you for your comments