This question was on the most recent sat mathematics level 2 test. if two spheres with unequal diameters intersect, what could be the intersection?
a. a point
b. a circle
c. a sphere
d. a point or a sphere
e. a circle or a sphere
99 points. provide a detailed and explanative answer.

It could be a point or a circle.

If the two spheres are tangent, then the intersection is by definition a point.

Since the two spheres are of unequal diameter, their intersection can't be a sphere (that can only happen if the spheres are of the same diameter and at the same point, then they overlap everywhere).

Now what happens if the two spheres are drawn close to each other a random way ? Well, they will intersect along a circle [see the image attached].

If you want more explanations/..., feel free to ask.

A Circle or point is your answer

See attached pictures