Let r be the radius of circle = OC = 8 cm.

∴ Diameter of the circle = AC = 2 × OC = 2 × 8 = 16 cm

Let a be the side of the square.

Now, according to the given condition,

Diagonal of square = Diameter of the circle.

Now in right angled triangle ACB,

(AC)² = (AB)² + (BC)²

(By Pythagoras theorem)

(16)² = a² + a²

⇒ 256 = 2a²

⇒ a² = 128

∴ Area of the square = a² = 128 cm²