Haven't had to converse in math-ese in a while, so please forgive my clumsy attempts to properly use terminology!
I've got a sphere of unknown radius, intersected by two parallel planes, creating circles A and B
I know radius of A
I know the length of a line drawn perpendicularly from origin of Circle A and through origin of Circle B to the sphere "shell"
Radius of A is larger than radius of B (i.e. above line does NOT go through origin of sphere)
I know the distance between the planes that create Circle A and Circle B, again measured perpendicularly.
Is it possible to find the radius of Circle B?
My specific numbers are a Circle A radius of 16.5, distance from outside of sphere to A is 9.4, and distance between A and B is 7.
$y = \sqrt{r^2 - x^2}$ (circle equation)
$r - 9.4 = \sqrt{r^2 - 16.5^2}$
$r^2 - 18.8r + 9.4^2 = r^2 - 16.5^2$
$18.8r = 16.5^2 + 9.4^2$
$r = 19.1814$ (the radius of the sphere)
$r - 16.4 = \sqrt{19.1814^2 - x^2}$
$2.7814^2 = 19.1814^2 - x^2$
$x = 18.9787$ (the radius of circle B)