Question

The area of the incircle of an equilateral triangle is 49π cm². Find the area of its circumcircle.

1. 196π cm²
2. 192π cm²
3. 49π cm²
4. 169π cm²

Answer 1

Correct Answer - Option 1 : 196π cm²

Given:

The area of the incircle of an equilateral triangle is 49π cm².

Formula used:

Inradius of equilateral triangle = a/(2√3)

Circumradius of equilateral triangle = a/(√3)

Where,

a = side of an equilateral triangle

Calculation:

Inradius of equilateral triangle = a/(2√3)

Area of incircle = π(a/2√3)²

⇒ π(a/2√3)²  = 49π

⇒ (a²)/12 = 49

⇒ a² = 49 × 12

⇒ a = 14√3

Circumradius of equilateral triangle = a/√3

⇒ (14√3)/√3

⇒ 14

Area of Circumcircle

⇒ π(14)²

⇒ 196π cm²

∴ Area of Circumcircle is 196π cm².