Question

In the given figure, O is the centre of a circle. If ∠OAB = 40° and C is a point on

the circle, then find ∠ACB.​

Answer 1

Answer:

50*

Step-by-step explanation:

In ΔQAB, OA = OB [both are the radius of a circle]

∠OAB = ∠OBA ⇒ ∠OBA = 40°

[angles opposite to equal sides are equal] Also, ∠AOB + ∠OBA + ∠BAO = 180°

[by angle sum property of a triangle]

∠AOB + 40° + 40° = 180°

⇒ ∠AOB = 180° – 80° = 100°

We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle.

∠AOB = 2 ∠ACB ⇒ 100° =2 ∠ACB

∠ACB = 100°/2 = 50°