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Circle Inscribed An Equilateral Triangle

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A circle is inscribed inside an equilateral triangle. If the circumference of the circle is 6m then the area of the triangle in cm squared is.

Hans007  Oct 22, 2017
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The radius of the circle  is

6  =  2pi * r

r =  6 / [ 2 pi]  = [ 3/pi] m

The center of the circle will lie on the angle bisectors....so

(1/2) the length of the base....call this "d"...... is given by

tan (30)  = [ 3/pi] / d

1/√3  = 3 / [pi *d ]  rearrange as

d = 3√3 / pi   m

And the height of the triangle, h, is given by

tan (60)  =   h / d

√3 = h / [3√3 / pi]

√3 = pi *  h /[ 3√3]  rearrange as

9/pi  m  = h

So....the area of the triangle is :

(1/2)b * h  =

d * h  =

[3√3 / pi] m * 9/pi m  =

[27√3] / pi^2  m ^2  ≈  4.738 m^2  ≈  4.738 * 100^2 cm^2 ≈ 47380 cm^2

CPhill  Oct 22, 2017

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