The sides of a regular triangle are 6√3cm. Calculate the length of a circle: a) circumscribed about

| September 6, 2021 | education

The sides of a regular triangle are 6√3cm. Calculate the length of a circle: a) circumscribed about this triangle b) inscribed in this triangle

Since each angle of a regular triangle is 60 °, the area of ​​this triangle is 6√3 * 6√3 * sin (60 °) / 2 = 108 * (√3 / 2) / 2 = 27√3.

Applying the formula for the area of ​​a triangle through the radius of the circumscribed circle, we find the radius R of the circle circumscribed about this triangle:

R = 6√3 * 6√3 * 6√3 / (4 * 27√3) = 216 * 3 * √3 / * (108√3) = 216 * 3/108 = 2 * 3 = 6.

Applying the formula for the area of ​​a triangle through the radius of the inscribed circle, we find the radius r of the circle inscribed in this triangle:

r = 27√3 / ((6√3 + 6√3 + 6√3) / 2) = 27√3 / (9√3) = 27/9 = 3.

Answer: the radius of the inscribed circle is 6, the radius of the inscribed circle is 3.



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