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in Circles by (44.3k points)

In the given figure, O is the centre of the circle and ∠AOB = 70°. Calculate the values of

(i) ∠OCA,

(ii) ∠OAC.

1 Answer

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by (58.8k points)
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Best answer

(i) We know that the angle subtended by an arc of a circle at the centre is double the angle subtended by the arc at any point on the circumference.

So we get

∠AOB = 2 ∠OCA

It is given that ∠AOB = 70o

We can write it as

∠OCA = 70o/2

By division

∠OCA = 35o

Therefore, ∠OCA = 35o.

(ii) From the figure we know that the radius is

OA = OC

We know that the base angles of an isosceles triangle are equal

∠OAC = ∠OCA

It is given that ∠OCA = 35o

So we get

∠OAC = 35o

Therefore, ∠OAC = 35o.

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