Extremal Dihedral on a Tangent Line

A line $BC$ is perpendicular to the plane of a unit circle $O$ and meets the circle at $A$, with $AB=BC=1$. Let $P$ be any point of the circle other than $A$, and let $l$ be the tangent to the circle $O$ at $P$. Determine, with proof, how many positions of $P$ make the dihedral angle $B\text{-}l\text{-}C$ attain its minimum, and how many make it attain its maximum.