SSC CHSL 16 Apr 2021 Shift 2 Paper

Section: Quantitative Aptitude

Question : 75 of 100

Marks: +1, -0

A

and

B

are two points on a circle with centre

O

C

is a point on the minor arc of the circle between points

A

and

B

. The tangents to the circle at

A

and

B

meet each other at a point

D

. If

∠ A D B=25^{∘}

, then

∠ A C B

(in degrees) is equal to

Solution:

Given,

∠ A D B=25^{∘}

∴

In quadrilateral

A O B D

∠ A O B=180^{∘}-25^{∘}=155^{∘}

∴

Other angle of

\;∠ A O B=360^{∘}-155^{∘}=205^{∘}

∴ \;\; ∠ A C B \;\; =\;{∠ A O B}/{2}

\{ ∵

Angle at the centre is twice the angle at the circumference

=\;{205}/{2}=102.5^{∘}

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