Q9

Let $A$ and $B$ be two distinct points in three-dimensional space. Let $M$ be the midpoint of $AB$.

Let $S_1$ be the set of all points $P$ such that $\overrightarrow{AP}\cdot\overrightarrow{BP}=0$.

Let $S_2$ be the set of all points $N$ such that $|\overrightarrow{AN}|=|\overrightarrow{MN}|$.

The intersection of $S_1$ and $S_2$ is the circle $S$.

What is the radius of the circle $S$?

A. $\dfrac{|\overrightarrow{AB}|}{2}$
B. $\dfrac{|\overrightarrow{AB}|}{4}$
C. $\dfrac{\sqrt3|\overrightarrow{AB}|}{2}$
D. $\dfrac{\sqrt3|\overrightarrow{AB}|}{4}$