Question 187
The vertical cross-section of a circular cone with vertex $P$ is an isosceles right-angled triangle. Point $A$ is on the circumference of the base circle, point $B$ is interior to the base circle, $O$ is the center of the base circle, $AB \perp OB$ and intersecting at $B$, $OH \perp PB$ and intersecting at $H$, $PA = 4$, and $C$ is the midpoint of $PA$. When the tetrahedron $O-HPC$ has the maximum volume, the length of $OB$ is ( ).