Hi, guys.. I know it is not a math forum, but could someone draw me this:
The first thing to realize is that this problem is about circles in
the plane, not about spheres in 3-dimensional space. You are only
interested in comparing a curve and a straight line, and they all lie
in the same plane. A plane through a sphere yields a circle. So we
just have to understand how a circle pulls away from a straight line.
Consider a circle of radius R, tangent to the x-axis at the origin and
the center on the negative y-axis. (I set it up this way in order to
simplify the calculation of the height which now will go straight up
the y-axis from the midpoint of line AB to the origin.) The equation
for such a circle is:
x^2 + (y+R)^2 = R^2
