Consider ABCD as a rectangle
We know that O is the point of intersection of the diagonals AC and BD
The diagonals of a rectangle are equal and bisect each other
So we get
OA = OB = OC = OD
We get O as the centre of the circle through A, B, C and D
Therefore, it is proved that the centre of the circle through A, B, C, D is the point of intersection of its diagonals.