Two congruent circles with centres O and O′ intersect at two points A and B. Then ∠AOB = ∠AO′B. Is the given statement true or false and justify your answer

Solution:

Consider the figure

Let us join AB, OA, OB, O’A and OB’

In triangle AOB and triangle AO’B

OA = AO’ (circles have same radius)

OB = BO’ (circles have same radius)

AB = AB (common chord)

From the SSS congruence criterion

Δ AOB ≅ Δ AO’B

∠AOB = ∠AO’B (cpctc)

Therefore, the statement is true.

✦ Try This: Two congruent circles with centres O and O′ intersect at two points P and Q. Then ∠POQ = ∠PO′Q.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 10

NCERT Exemplar Class 9 Maths Exercise 10.2 Problem 3

Two congruent circles with centres O and O′ intersect at two points A and B. Then ∠AOB = ∠AO′B. Is the given statement true or false and justify your answer

Summary:

The statement “Two congruent circles with centres O and O′ intersect at two points A and B. Then ∠AOB = ∠AO′B” is true

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