Solution
= Solution
The <sphere-plane intersection> is governed by the <orthogonal projection> of the <sphere>'s centre onto the <plane>. Since $\mathbf n$ has unit length, let $h=p-\mathbf n\cdot\mathbf c$, the signed distance from $\mathbf c$ to the <plane> along $\mathbf n$. The following parts determine the centre and radius and retain this sign; the radii alone cannot distinguish the two possible sides of the oriented <plane>.