From a point $P$ on the circle $x^{2} + y^{2} = 4r^{2}$, tangents are drawn to $x^{2} + y^{2} = r^{2}$ at $Q$ and $R$. Then which of the following statement(s) are true regarding the centroid of $ΔPQR$
$A.$ is at a distance $r$ from chord $QR$.;
$B.$ lies on $x^{2} + y^{2} = r^{2}$
$C.$ is at a distance $1.5r$ from $P$
$D.$ doesn't lie on the line joining the origin and $P$
My take: $B$
Please help.