Question

Question 3
Write True or False and justify your answer :

The congruent circles with centres O and O' intersect at two points A and B. Then $\angle AOB=\angle A{O}^{\prime }B$.

Answer 1

True

Two congruent circles mean that their radii are equal.

Join AB, OA, OB, O' A and BO'.
In $\Delta AOBand\Delta A{O}^{\prime }B$,
OA = AO' [both circle have same radius]
OB = OB' [both circles have same radius]
And AB = AB [common]
$\therefore \Delta AOB\cong \Delta A{O}^{\prime }B$ [by SSS congruence rule]
$\Rightarrow \angle AOB=\angle A{O}^{\prime }B$ [by CPCT]