Question

iv) O is the circumcentre of triangle ABC and angle OAB = 50°, then the value of angle
ACB is
(a) 50° (b) 100° (c) 40° (d) 80°​

Answer 1

Answer:

AO and OB are radii of the circle.

side AO=BO so, ∠OAB=∠OBA [Isosceles triangle AOB]

Angle subtended by chord at the centre of a circle is double of the angle subtended at it's circumference.

Therefore ∠AOB=2∠ACB

∠AOB=100

∘

In triangle AOB

The sum of all three angle will be 180

∘

So, ∠AOB+∠OBA+∠OAB=180

∘

100

∘

+∠OBA+∠OAB=180

∘

100

∘

+2∠OAB=180

∘

[∠OAB=∠OBA]

∠OAB=

2

80

∘

∠OAB=40

∘