In a rectangle $ABCD$, the coordinates of $A$ and $B$ are $(1,2)$ and $(3,6)$ respectively and some diameter of the circumscribing circle of $ABCD$ has equation $2x-y+4=0$. Then the area of the rectangle is:
My work: I found the equations of $AD$ and $BC$ of the rectangle. Taking the points $C$ and $D$ as $(x_1,y_1)$ and $(x_2,y_2)$ I wrote the equation for $AD=BC$. I think that the equation given for the diameter of the circle should pass through the point of intersection of the diagonals of the rectangle and wrote equation for the point of intersection. This gives me two equations and four unknowns. I know there is some problem with my method making the answer to this problem hard. So, please help me do the problem by the right method.