What shape does the intersection of 2 spheres make

i know its a circle, but why is it circle.. isn't it just a weird () shape? can you please explain and thank you

It could also actually be a point or a sphere (if they are concentric spheres with the same radius.

To demonstrate, take two apples, and slice them each in roughly the same way. The area that was sliced is a circle, right? If you put those two apples together, they can both fit onto the same circle.

Well, that's about the best I can do.
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let one sphere be x² + y² + z² = 9, a sphere of radius 3, center at the origin,
and let the other be x² + y² + (z – 4)² = 4, a sphere of radius 2 with center at (0,0,4), which is 1 unit outside of the 1st sphere. so we know they intersect.

subtract the equations, get
z² – (z – 4)² = 5
z² – z² + 8z – 16 = 5
8z = 21
z = 2.625
plug that back into the other equations
x² + y² + (2.625)² = 9
x² + y² = 2.109375
and
x² + y² + (2.625 - 4)² = 4
x² + y² = 2.109375
which are equations of the same circle in the z = 2.625 plane

Visualize it as if the two spheres were soap bubbles; and they were just touching.
Then the intersection would be a point.

Now start pushing the soap bubbles together.
Then the intersection becomes a ring. ... or ... a circle.