Past exam of the mathematical methods I course of the University of Oxford / 2017 / 10 / c / ii / Solution

Let $s=(x_0,y_0,z_0)$ be the sphere centre. The circle centre is its perpendicular projection onto the plane:For the specific plane this isFor a point on the section, its displacement from $h$ lies in the plane and is perpendicular to $s-h$. The Pythagorean theorem therefore givesA genuine circle requires $d<R$. At $d=R$ the section is a single tangent point, and at $d>R$ the plane misses the sphere. A central cut $d=0$ gives a great circle of radius $R$.