UPSC CDS I 2025 Mathematics Paper

Radius of the circle (r)=2cm
The circle is inscribed in an equilateral triangle.
Formula used:
Area of an equilateral triangle =‌

√‌3

4

a2
Where, a= side of the equilateral triangle
Relation between radius (r) and side (a) of an equilateral triangle:
r=‌

√‌3

6

a
‌r=‌

√‌3

6

a
‌⇒2=‌

√‌3

6

a
‌⇒a=‌

2×6

√‌3

=‌

12

√‌3

=4√‌3
Area of the triangle:
‌‌ Area ‌=‌

√‌3

4

a2
‌⇒‌ Area ‌=‌

√‌3

4

(4√‌3)2
‌⇒‌ Area ‌=‌

√‌3

4

×16×3
‌⇒‌ Area ‌=12√‌3