Question

3.
A circle with radius 20 cm is inscribed in an equilateral triangle. Find the sides of the
triangle.
of the diagonals.​

Answer 1

Given info : A circle with radius 20cm is inscribed in an equilateral triangle.

To find : the sides of the triangle are ..

solution : when a triangle is inscribed in a circle then centre of circle is circumcenter of that triangle.

and we know, the relation between radius of circle and side of triangle.

it is given by, R = abc/4∆

here triangle is equilateral.

so, a = b = c = x (let)

and area of equilateral triangle = √3/4 x²

so, R = x³/4(√3/4 x²) = x/√3

given R = 20 cm

⇒20 = x/√3

⇒x = 20√3 cm

Therefore each side of equilateral triangle is 20√3 cm.

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Answer 2

$\huge \tt s = 20 \sqrt{3} \: cm$