Find the coordinates of $B$

Question

We have triangle $ABC$, right angled at $B$. $A(2,5)$ and $C(-2,3)$. Using analytical geometry to find the coordinates of $B$. Well, I have tried drawing a circled centred at the Midpoint of AC i.e. $X(0,4)$. Also the radius of that circle is $\sqrt5$. So, I need to find the coordinates of the point lying on the diagonal $BD$ which is $\sqrt5$ units away from $X$. But I couldn't find the coordinates. How can I do it? Well, as it seems my method is not efficient. Pls suggest some better procedure.