Question 78

What is the length of the radius of the circumcircle of the equilateral triangle, the length of whose side is $$6\sqrt{3}$$ cm ?

Solution

Area of an equilateral triangle = $$ \frac{\sqrt3}{4} \times a^2 $$

a = side of the triangle

length of the radius of a circumcircle in an equilateral triangle

$$ R = \frac{abc}{4 \times area of equilateral triangle} $$

$$ R = \frac{ 6\sqrt3 \times 6\sqrt3 \times 6\sqrt3}{ 4 \times \frac{\sqrt3}{4} \times 6 \sqrt3 \times 6 \sqrt3} $$

= 6

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