UPSC CDS 2 2022 Math Paper

The angle at the centre of the polygon =‌

360∘

n

Where n is the number of sides
tan‌θ=‌

‌ Perpendicular ‌

‌ base ‌

The angle at the centre of a polygon of n sides =‌

360∘

n

The angle at the centre of the polygon of 15 sides =‌

360∘

15

=24∘
As OC is the radius \& AB is the tangent, hence
∠OCA=∠OCB=90∘
Therefore, △OAC is the right-angled triangle
tan‌12∘=‌

AC

OC

=‌

1

2(OC)

⇒2‌OC=‌

1

tan‌12∘

=cot‌12∘
⇒‌ Diameter ‌=cot‌12∘‌‌[∵‌ diameter ‌=2‌ radius ‌]