In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of :(i) ∠AOB(ii) arc AB(iii) ∠ACB[Figure: circle with centre O; chord AB below the centre, C on the major arc…

Q.3 (A)(2) In the following figure, point O is the centre of the circle and length of chord AB is equal to the radius of the circle. Find the measures of :

(i) ∠AOB
(ii) arc AB
(iii) ∠ACB

[Figure: circle with centre O; chord AB below the centre, C on the major arc AB above the centre; seg OA, seg OB, seg CA and seg CB drawn.]

by completing the activity.

Activity :

In \(\Delta AOB\),

AO = OB = AB

\(\therefore \Delta AOB\) is an ____ triangle.

\(\therefore m\angle AOB = ____\)

\(m\angle AOB = m(\text{arc AB}) = ____\) ......... (definition of measure of an arc)

\(m\angle ACB = \dfrac{1}{2} \times ____\) ......... (inscribed angle theorem)

\(= \dfrac{1}{2} \times 60^\circ\)

\(m\angle ACB = ____\)