SSC CGL 18 Aug 2021 Shift 3 Paper

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Question : 54 of 100

Marks: +1, -0

Points

A

and

B

are on a circle with centre

O

. Point

C

is on the major arc

A B

. If

∠ O A C=35^{∘}

and

∠ O B C=45^{∘}

, then what is the measure (in degrees) of the angle subtended by the minor arc

A B

at the centre?

70
$160 \;\;$
80
100

Solution:

Given,

∠ O A C \;\; =35^{∘}, \;\text " and "\; ∠ O B C=45^{∘}

O C \;\; =O A=O B=\;\text " radius "\;

Then,

∠ O A C=∠ O C A=35^{∘}

And

∠ O B C=∠ O C B=45^{∘}

So,

∠ A C B=∠ O C A+∠ O C B

⇒ \;\; ∠ A C B=35^{∘}+45^{∘}=80^{∘}

∴ \;\; ∠ A O B=2 × ∠ A C B

[ ∵

Central angle is twice of circumference angle]

=2 × 80^{∘}=160^{∘}

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