In the figure,
As AC and BD bisect each other
Therefore, AC and BD are the diagonals of the parallelogram.
> ABCD is a parallelogram
> angle A = angle C
angle B = angle D
But, ABCD is a cyclic quadrilateral
Therefore, angle A + angle C = 180 degree
angle B + angle D = 180 degree
> 2 angle A = 180 degree
2 angle B = 180 degree
> angle A = 90 degree angle B = 90 degree
So, angle A = angle B =angle C = angle D = 180 degree
Therefore, ABCD is a rectangle and diagonals AC and BD are diameters.