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In the given figure, O is the centre of the circle. If ACB=50

Question

In the given figure, $O$ is the centre of the circle. If $∠ A CB = 5 0^{o}$ , find $∠ O A B$ .

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Sebastian Discussed

In the given figure,

O

is the centre of the circle. If

∠ A CB = 5 0^{o}

, find

∠ O A B

13 mins ago

Discuss this question LIVE

13 mins ago

Text solutionVerified

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

∠ A OB = 2∠ A CB

It is given that

∠ A CB = 5 0^{o}

By substituting

∠ A OB = 10 0^{o} .... (1)

Consider

△ O A B

We know that the radius of the circle are equal

O A = OB

Base angles of an isosceles triangle are equal

So we get

∠ O A B = ∠ OB A .... (2)

Using the angle sum property

∠ A OB + ∠ O A B + ∠ OB A = 18 0^{o}

Using equation

(1)

and

(2)

we get

10 0^{o} + 2∠ O A B = 18 0^{o}

By subtraction

2∠ O A B = 18 0^{o} - 10 0^{o}

So we get

2∠ O A B = 8 0^{o}

by division

∠ O A B = 4 0^{o}

Therefore,

∠ O A B = 4 0^{o}

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Question Text	In the given figure, $O$ is the centre of the circle. If $∠ A CB = 5 0^{o}$ , find $∠ O A B$ .
Answer Type	Text solution:1
Upvotes	150

In the given figure, O is the centre of the circle. If ∠ACB=50o, find ∠OAB.

Text solutionVerified

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In the given figure, $O$ is the centre of the circle. If $∠ A CB = 5 0^{o}$ , find $∠ O A B$ .