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Circles — MATHS STD 9 — Question

Rajasthan BoardEnglish MediumSTD 9MATHSCircles1 Mark
Question
Write True or False and justify your answer in the following:
Two congruent circles with centres O and O′ intersect at two points A and B. Then $\angle\text{AOB}=\angle\text{AO'B}.$
✓

Answer

True.
Solution:

Join AB and OB, O'A and BO'.
In $\triangle\text{AOB}$ and $\triangle\text{AO'B,}$
OA = AO' [both circles have same radius]
OB = BO' [both circles have same radius]
and AB = AB [common chord]
$\triangle\text{AOB}=\triangle\text{AO'B}$ [by SSC congruence rule]
$\Rightarrow\angle\text{AOB}=\angle\text{AO'B}$ [by CPCT]

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