In the figure, A, B and C are points on a circle with centre O. Point C lies on the major arc AB, and ∠ACB = 40°. Seg OA and seg OB are drawn. Complete the following activity to find m(arc AB) and ∠AOB.[Figure: a circle with centre O; chord AB near t…

Q.2 (A)(1) In the figure, A, B and C are points on a circle with centre O. Point C lies on the major arc AB, and ∠ACB = 40°. Seg OA and seg OB are drawn. Complete the following activity to find m(arc AB) and ∠AOB.

[Figure: a circle with centre O; chord AB near the bottom of the circle; point C on the upper (major) arc; seg CA and seg CB form the inscribed angle ∠ACB = 40°; radii OA and OB form the central angle ∠AOB.]

Solution :

∠ACB is an inscribed angle intercepting arc AB.
∴ m∠ACB = ½ × m(arc ____) .................... (inscribed angle theorem)
∴ m(arc AB) = 2 × ____ = ____
∠AOB is the central angle of arc AB.
∴ m∠AOB = m(arc AB) = ____