Ray Sphere Intersection
A [see page 6, way] to detect whether a sphere intersects a line.
There's the classic [see page 7, algebraic] approach (trying to solve for the roots of a quadratic formula) but also the slightly quicker [see page 8, geometric] approach which finds the line perpendicular to the ray and going through the centre of the circle and then asserts whether it's within the bounds of the radius.