Let $C$ be a circle passing through the points $A(2,-1)$ and $B(3,4)$. The line segment $A B$ is not a diameter of $C$. If $r$ is the radius of $C$ and its centre lies on the circle $(x-5)^2+(y-1)^2=\frac{13}{2}$, then $r^2$ is equal to :
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