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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

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by janenajane

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(i) AC and BD are diameters.

(ii) ABCD is a rectangle

by janenajane

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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...........

The Brainliest Answer!

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.