Can ne 1 help me how to find the centre (Xc,Yc) for an arc having end points A(x1,y1)[say (2,5)] and B(x2,y2)[say (6,2)]?.........

I tried to calculate the centre imagining those end points of an arc as the end points of the diagonal of a square..........If we assume that the side of the square as 'a' then it becomes the radius 'r' for the arc which i found to be 5/sqrt(2) units with the given points (2,5) and (6,2)

The problem is, even if I knew the radius and the end points i'm unable to calculate the center C(Xc,Yc)...........

Was my calculation wrong or the approach was wrong?

And i also want to find the length 'l' of the arc and height 'h' of the curved surface................Please help me out.

I'm sending the figure as an attachment for clear picture of what i'm asking.