SSC CGL 17 Aug 2021 Shift 1 Paper

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Question : 61 of 100

Marks: +1, -0

In a circle with centre

O

.

P A X

and

P B Y

are the tangents to the circle at points

A

and

B

, from an external point

P . Q

is any point on the circle such that

∠ Q A X=59^{∘}

and

∠ Q B Y=72^{∘} .

What is the measure of

∠ A Q B

?

$31^{∘}$
$72^{∘}$
$49^{∘}$
$59^{∘}$

Solution:

Given,

P A X

and

P B Y

are tangents.

∠ Q A X=59^{∘}, ∠ Q B Y=72^{∘}

By alternate segment theorem

\;\text " If "\;\;∠ Q B Y=72^{∘}

\;\text " then, "\;\;∠ Q A B=72^{∘}

\;\text " Similarly, "\;\;∠ Q A X=59^{∘}

\;\text " and "\;\;∠ Q B A=59^{∘}

⇒\;∠ Q A B+∠ Q B A+∠ A Q B=180^{∘}

⇒\;72^{∘}+59^{∘}+∠ A Q B=180^{∘}

⇒\;∠ A Q B=180^{∘}-72^{∘}-59^{∘}

⇒\;∠ A Q B=49^{∘}

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