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An equilateral triangle of side √3cm is inscribed i...

An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.

A.

2/3 cm

B.

2 cm

C.

1 cm

D.

3 cm

Correct answer is C

Since the inscribed triangle is equilateral, therefore the angles at all the points = 60°

Using the formula for inscribed circle, 

2R = \(\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}\)

where R = radius of the circle; a, b and c are the sides of the triangle.

⇒ 2R = \(\frac{\sqrt{3}}{\sin 60}\)

 2R = \(\frac{\sqrt{3}}{\frac{\sqrt{3}}{2}}\)

2R = 2

R = 1cm