This is the question: Let $S$ be the sphere of radius $14$ centered at the point $C(5, −3, 16)$. (a) The plane $y = 3$ intersects $S$ in a circle. Where is the centre of this circle and what is its radius?
The center is easy to calculate, $(5,3,16)$ I have no clue of how to get the radius though.
We determine the distance of the points $C(5/-3/16)$ and $(5/3/16)$ , which is $6$ and denote it with $d$ ( d is the distance of $C$ from the plane). Then, the radius of the circle is $r'=\sqrt{r^2-d^2}=\sqrt{14^2-6^2}=\sqrt{160}=12.649$