jmc

We use coordinates. Let the circle have center $(0,0)$ and radius $\sqrt{50}$; this circle has equation $x^2+y^2=50$. Let the coordinates of $B$ be $(a,b)$. We want to find $a^2+b^2$. $A$ and $C$ with coordinates $(a,b+6)$ and $(a+2,b)$, respectively, both lie on the circle. From this we obtain the system of equations $a^2+(b+6{)}^2=50$ $(a+2{)}^2+b^2=50$ Solving, we get $a=5$ and $b=-1$, so the distance is $a^2+b^2=\boxed{26}$.