Question

Prove that the centre of the circle circumscribing the cyclic rectangle ABCD is the point of intersection of its diagonals.

Answer 1

Let O be the circle circumscribing the cyclic rectangle ABCD. 

Since, 

∠ABC = 90°and AC is the chord of the circle. 

Similarly, 

BD is a diameter 

Hence, 

Point of intersection of AC and BD is the centre of the circle.