Given that we need to find the centre of the circle inscribed square.

It is also told that x = 2, x = 6, y = 5 and y = 9 are the sides of a square.

Let us assume A,B,C,D are the vertices of the square. On solving the lines we get the vertices as:

⇒ A = (2,5)

⇒ B = (6,5)

⇒ C = (6,9)

⇒ D = (2,9)

Since the diagonal of the square is diameter of circle as the circle circumscribes the square.

So, taking any diagonal as diameter gives the same centre of the circle.

Let us assume diagonal AC as the diameter.

We know that centre is the mid - point of the diameter.

⇒ Centre(C) =

⇒ C = (4,7)

∴The coordinates of the centre is (4,7).