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What is the perimeter of an equilateral triangle inscribed in a?

What is the perimeter of an equilateral triangle inscribed in a circle of a radius 2? In general, what is the formula for the perimeter (and area) of the triangle with an inscribed circle of a radius r? Moreover, if the circle of radius r is inscribed in the equilateral triangle, what would the triangle's perimeter and area be? I think I could use Heron's formula for the area if the perimeter is derived. I think this could be solved in terms of trig. function.

Public Comments

1. it is 3 pi radical 3 of the radius, so in this case, the perimeter of the triangle is 6pi, radical 3
2. The length of one side of the inscribed equilateral triangle is the same as the diameter or 2r. 2r = 4 There are 3 sides on the triangle: 4*3 = 12 Therefore, the perimeter is 12 units
3. first u take the square root of pie and divide it by nine then u multiply that by 33 to get the radius then divide that # by 47 multiply by 15 add 300......
4. s = r^2 + r^2 -2r^2r^2cos(2π/3) = 2r^2-2r^4cos(2π/3) =2(2)^2-2(2)^4cos(2π/3) =8-32(-1/2) =8+16 =34 p = 34*3 =102 i believe that is the correct answer
5. For an equilateral triangle inscribed in a circle or radius r the perimeter P = 3*sqrt(3)*r and the area A = 3*sqrt(3)*r^2/4. In this particular instance, since r = 2, the perimeter is P = 6*sqrt(3) and the area is A = 3*sqrt(3). [The three medians of the equilateral triangle intersect at a point 2/3 the way from a vertex, hence the radius r of such a circle is 2/3 the height of the equilateral triangle. Use the properties of a 30-60-90 triangle to determine the base of the equilateral triangle then solve for perimeter=3*(baselength) and area=(1/2)(base)(height).] For an equilateral triangle circumscribed in a circle of radius r the perimeter P = 6r*sqrt(3) and the area is A = 3*sqrt(3)*r^2. [Here, the radius r of such a circle is 1/3 the height of the equilateral triangle. Again, use the properties of a 30-60-90 triangle to determine the base of the equilateral triangle and then find the perimeter and area as before.]