A regular triangle is inscribed in a circle whose radius is 6 cm. Calculate the radius of a circle circumscribed
| March 3, 2021 | education
A regular triangle is inscribed in a circle whose radius is 6 cm. Calculate the radius of a circle circumscribed about a square whose side is equal to the side of the triangle.
Using the formula an = 2Rsin (180 ° / n) to calculate the side length of a regular n-gon inscribed in a circle with radius R, we find the side length of a triangle.
n = 3.
a3 = 2Rsin (180 ° / 3) = 2Rsin60 ° = 2√3R / 2 = √3R.
The length of the side of the triangle a = √3 * 6 = 6√3 (cm).
a4 = 2Rsin (180 ° / 4) = 2Rsin45 ° = 2R√2 / 2 = √2R.
Because the side of the square is equal to the side of the triangle, then:
6√3 = √2R.
R = 6√3 / √2 = 6√3 * √2 / (√2 * √2) = 6√6 / 2 = 3√6 (cm).
Answer: R = 3√6 (cm).
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