Quadrilateral ABCD has vertices at A(13, 9), B(14, 2), C(7, 1), and D(5, 5). Show that ABCD is cyclic.

I didn't know how to do it without graph paper so I drew the quadrilateral on a graph and said that the diagonals represent the diameter of a circle with the intersection of the diagonals representing the centre of the circle. Half a diagonal also represents the radius of the circle.

I think that this might be correct but I am unsure.