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  • Write True or False and justify your answer in each of the following: Two congruent circles with centres O and {O}' intersect at two points A and B. Then \angle AOB =\angle A{O}'B.

Write True or False and justify your answer in each of the following: Two congruent circles with centres O and {O}' intersect at two points A and B. Then \angle AOB =\angle A{O}'B.

Answers (1)

True

Solution:

Two congruent circles with centres O and {O}' intersecting at two points A and B are shown in the above figure.

These are congruent circles, it means that their radius is the same.

If the figure, we have joined the centres O and {O}'

In \triangle OA{O}' \: \: and\: \: \triangle OB{O}'

OA = {O}'A  (Radius)

So, \angle AO{O}' =\angle A{O}'O   

(angles opposite to equal sides in a triangle are equal)  …(i)

Similarly, in \triangle OB{O}'

OB= {O}'B   (Radius)

\angle BO{O}' =\angle B{O}'O (angles opposite to equal sides in a triangle are equal)            …(ii)

Adding (i) and (ii)

\angle AO{O}' +\angle BO{O}' =\angle A{O}'O+\angle B{O}'O

\angle AOB =\angle A{O}'B

Therefore the given statement is true.

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