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