SSC CHSL 6 Aug 2021 Shift 1 Paper

Section: Quantitative Aptitude

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Question : 62 of 100

Marks: +1, -0

P A

and

P B

are tangents drawn to

a

circle with centre

O

from an external point

P

. If

A

and

B

are points on the circle and

∠ O B A=42^{∘}

, then

∠ A P B

is

$78^{∘}$
$84^{∘}$
$76^{∘}$
$86^{∘}$

Solution:

Given,

Since,

P A

and

P B

are tangents at

A

and

B

, respectively.

∴ ∠ P A O=∠ P B O=90^{∘}

Since,

∠ O B A=42^{∘} \;\text " (Given "\;)

∴ \;∠ P B A=∠ P A B=90^{∘}-42^{∘}=48^{∘}

\;\; \{ ∵ O A=O B=\;\text " radius "\;\}

∴ \;\ln △ P A B,

\;∠ A P B=180^{∘}-(48^{∘}+48^{∘})=84^{∘}

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