The height of an equilateral triangle is 9 cm, find the circumference inscribed in this triangle.

The height of an equilateral triangle is

h = (√3 / 2) * a, where a is the length of the side of the triangle.

From here

a = 2h / √3.

Find the side of the triangle:

a = (2 * 9) / √3 = 18 / √3 = 18√3 / 3 = 6√3 cm.

the radius of the inscribed circle is

r = a√3 / 6.

Find the radius:

r = (6√3 * √3) / 6 = (6 * 3) / 6 = 3 cm.

The circumference is calculated using the following formula:

l = 2πr.

Let’s find it:

l = 2π * 3 = 6π ≈ 18.85 cm.

Answer: the length of a circle inscribed in an equilateral triangle is approximately 18.85 cm.