SSC CHSL 12 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

© examsiri.com

Question : 61 of 100

Marks: +1, -0

A B

and

A C

are tangents to a circle with centre

O

from an external point

A

. The tangents

A B

and

A C

touch the circle at

B

and

C

, respectively, such that

∠ B A C=118^{∘}

. Find the measure of

∠ O C B

.

$59^{∘}$
$62^{∘}$
$60^{∘}$
$54^{∘}$

Solution:

Given,

Since,

A B

and

A C

are tangent on radii point

B

and

C

on the circle.

∠ O B A=∠ O C A=90^{∘}

∴ ∠ B O C=360^{∘}

\;\;\; -(90^{∘}+90^{∘}+118^{∘})=62^{∘}

\;\text " In "\; △ O B C, \;\; ( ∵ O B=O C=\;\text " radius "\;)

∠ O C B=∠ O B C

∴ ∠ O B C+∠ O C B+∠ B O C=180^{∘}

∠ O C B+∠ O C B+62^{∘}=180^{∘}

2 ∠ O C B=180^{∘}-62^{∘}=118^{∘}

∴ ∠ O C B=\;{118^{∘}}/{2}=59^{∘}

© examsiri.com

Go to Question:

Prev Question

Next Question