# Finding if two sphere's intersect method

• SanEng02
In summary, the method of solving whether or not two spheres intersect involves finding the centers and radii of each sphere, and then determining if the distance between the centers is less than or equal to the sum of the radii. If so, the spheres will intersect. However, it is important to note that this method assumes the spheres have equal radii and in the general case, they may not.
SanEng02
Hi I was just curious if this method of solving whether or not two spheres intersect is a viable method that will give me the correct answer. Say if I am given the two equations of the sphere's is it viable to:
• Find the centre and radius of each sphere.
• Find the magnitude of the distance of the line between the sphere's centres
• If (magnitude distance of line) > radius they do not intersect, if (magnitude distance of the line) ≤ radius they do intersect.
From what I'm reading in the book and my notes, I think this should work.

Last edited:
SanEng02 said:
• If (magnitude distance of line) > radius they do not intersect, if (magnitude distance of the line) ≤ radius they do intersect.
Almost. Two points:
1. You assume that the spheres have the same radii. In the general case, they might not.
2. Assume that the spheres just barely touch. Then the distance from the center of each sphere to the touching point is equal to the radius of that sphere ∴ The distance between the centers is equal to the sum of the radii. Therefore, if the distance between the centers is less than the sum of the radii, the spheres will intersect.

Svein said:
Almost. Two points:
1. You assume that the spheres have the same radii. In the general case, they might not.
2. Assume that the spheres just barely touch. Then the distance from the center of each sphere to the touching point is equal to the radius of that sphere ∴ The distance between the centers is equal to the sum of the radii. Therefore, if the distance between the centers is less than the sum of the radii, the spheres will intersect.

In this case the radii were the same but I forgot to mention that but I knew I was missing something. Thanks!

Even in that case, your statement was wrong. Given two spheres of equal radii, they will intersect if and only if the distance between their centers is less than or equal to two times their common radius.

Right, that makes even more sense thanks!

## 1. How do you determine if two spheres intersect?

To determine if two spheres intersect, we can use the distance formula to calculate the distance between their centers. If this distance is less than or equal to the sum of their radii, then the spheres intersect.

## 2. Can two spheres intersect at more than one point?

Yes, two spheres can intersect at more than one point. This occurs when the distance between their centers is less than the difference between their radii, but greater than the sum of their radii.

## 3. What is the equation for finding the distance between two points?

The distance formula, also known as the Pythagorean theorem, is: d = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2), where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points.

## 4. Can two spheres with the same center intersect?

No, two spheres with the same center cannot intersect. In order for two spheres to intersect, they must have different centers and their radii must be large enough to reach each other.

## 5. Are there any special cases when determining if two spheres intersect?

Yes, there are a few special cases to consider when determining if two spheres intersect. These include when one sphere is completely inside the other, when one sphere is tangent to the other, and when the centers of the spheres are collinear.

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