A circle is inscribed in a equilateral triangle of side a. The area of the circle is

Question

A circle is inscribed in a equilateral triangle of side a. The area of the circle is (A)  3π a2 sq unit (B)  2a2 sq unit (C)  a2 sq unit (D) None of these

Tardigrade Admin · Accepted Answer

In an equilateral triangle length of median CD=(√3/2)a. Also, centroid of triangle lies on the centre of circle. ∴ OC=2× (√3/2)a=√3a ∴ Area of circle = π (OC)2 =3π a2 sq unit

Q. A circle is inscribed in a equilateral triangle of side a. The area of the circle is

$3 π a^{2}$ sq unit

$2 a^{2}$ sq unit

$a^{2}$ sq unit

None of these

In an equilateral triangle length of median $C D = \frac{3}{2} a .$
Also, centroid of triangle lies on the centre of circle.
$∴$ $OC = 2 \times \frac{3}{2} a = 3 a$
$∴$ Area of circle = $π (OC)^{2}$
$= 3 π a^{2} s q u ni t$

Q. A circle is inscribed in a equilateral triangle of side a. The area of the circle is

3πa2 sq unit

2a2 sq unit

a2 sq unit

None of these

In an equilateral triangle length of median CD=23​​a. Also, centroid of triangle lies on the centre of circle. ∴ OC=2×23​​a=3​a ∴ Area of circle = π(OC)2 =3πa2squnit

$3 π a^{2}$ sq unit

$2 a^{2}$ sq unit

$a^{2}$ sq unit

In an equilateral triangle length of median $C D = \frac{3}{2} a .$
Also, centroid of triangle lies on the centre of circle.
$∴$ $OC = 2 \times \frac{3}{2} a = 3 a$
$∴$ Area of circle = $π (OC)^{2}$
$= 3 π a^{2} s q u ni t$