# What is the intersection of two balls in $\mathbb{R}^3$?

I know that the What is the intersection of two balls in $\mathbb{R}^2$ is either 0,1 or 2 points (since a ball in $\mathbb{R}^2$ is just a circle I can drew this).

What is the intersection of two balls in $\mathbb{R}^3$ ? is it at max 3 points ?

I would also like to know about the more general case of $n>1$

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Two spheres will intersect in a circle. Possibly with zero or imaginary radius. –  Ｊ. Ｍ. Apr 28 '12 at 9:50
A ball is often taken to mean the interior of a sphere, perhaps including the edge, which would make their intersections a lens –  Henry Apr 28 '12 at 9:59