Question

4. AC and BD are two chords of a circle which bisect each other. Prove that :
(i) AC and BD are diameters.
(ii) ABCD  is a rectangle

Answer 1

AC and BD bisects each other
therefore it is a paralleogram
we know that a cyclic parallelogram is rectangle

as ∠A = ∠B=∠C=∠D=90°

there fore AC and BD are diameters

Hope this helps...........

Answer 2

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.