Quadratic intersections

I should probably put this in my sig - I''m not a math whiz so my question may seem awkwardly stupid for the less challenged ones in algebra. My question is this: after following this procedure... 1) intersect ray A with sphere S, getting two real intersection points I_n and I_f (n and f stand for near and far) 2) intersect ray B with S, the end point being I_n, getting another pair real intersection points J_n and J_f ... how do I determine whether I_n == J_n or I_n == J_f? Since I''m not a complete monkeyape, I tried the obvious: I compared VecDistance(B, J_n) to VecDistance(B, I_n), but the results were not what I expected (it would seem I''m a monkeyape after all). Anyway - when I intersect ray B from point P1 to I_n, which is a point on the sphere, am I supposed to get one intersection point or two? I tried it either way and the result is never what I would expect. Can someone point out what I''m doing wrong here? I guess the question is a bit vague, but it''s probably best if someone smarter asked the questions and I tried to explain what I''m doing...