a sphere intersects a plane that is 6 units away from its center; the intersection is a circle of radius 8. what is the radius of the sphere?

Let K be the center of the sphere.
Let L be the center of the circle of intersection.
Let M be any point on the circle of intersection.

Those three points form a right triangle.
∠KLM = 90° ... (by symmetry)
KL = 6 ... (given)
LM = 8 ... (given)
KM = radius of the sphere

You are familiar with the Pythagorean theorem, right?...Show more