$Δ A B C$ is an equilateral triangle with side length $12$ cm. The radius of the inscribed circle is:

Open in App

Solution

$Δ$ rs, where, $r -$ inradius, $s -$ semiperimeter of triangle.
Side length of $△ A B C, a = 12$ cm
Radius of inscribed circle $= \frac{\sqrt{3}}{2} \times \frac{1}{3} \times a$
$= \frac{\sqrt{3}}{2} \times \frac{1}{3} \times 12$ cm
$= 2 \sqrt{3}$ cm

Suggest Corrections

Similar questions

Q. An equilateral

Δ

ABC of side 6 cm is inscribed in a circle. Find the radius of the circle.

Q. A circle is inscribed in an equilateral triangle ABC with side

12

cm, touching its sides. Find the radius of the inscribed circle and the area of the shaded part.

A circle is inscribed in an equilateral triangle ABC is side 12 cm, touching its sides (Fig). Find the radius of the inscribed circle and the area of the shaded part.

An equilateral triangle ABC is inscribed in a circle of radius 12 cm, which is centered at O, as shown below. Calculate the length of the sides of this triangle.

Q. Find the length of side of an equilateral triangle inscribed in a circle of radius 4 cm. (

\sqrt{3} = 1.73

)

Join BYJU'S Learning Program

ΔABC is an equilateral triangle with side length 12 cm. The radius of the inscribed circle is:

Δrs, where, r− inradius, s− semiperimeter of triangle.Side length of △ABC,a=12 cmRadius of inscribed circle =√32×13×a=√32×13×12 cm=2√3 cm

$Δ A B C$ is an equilateral triangle with side length $12$ cm. The radius of the inscribed circle is:

$Δ$ rs, where, $r -$ inradius, $s -$ semiperimeter of triangle.
Side length of $△ A B C, a = 12$ cm
Radius of inscribed circle $= \frac{\sqrt{3}}{2} \times \frac{1}{3} \times a$
$= \frac{\sqrt{3}}{2} \times \frac{1}{3} \times 12$ cm
$= 2 \sqrt{3}$ cm