A triangle is inscribed in a circle of radius $1$. The distance between the orthocenter and the circumcenter of the triangle cannot be

$PA$ and $PB$ are tangents to a circle $S$ touching it at points $A$ and $B$. $C$ is a point on $S$ in between $A$ and $B$ as shown in the figure. $LCM$ is a tangent to $S$ intersecting $PA$ and $PB$ on points $L$ and $M$, respectively. Then the perimeter of the triangle $PLM$ depends on

$\left(1,2\sqrt{2}\right)$ is a point on circle $x^2+y^2=9$. Which of the following is not a point on the circle at $2$ units distance from $\left(1,2\sqrt{2}\right)$?