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A regular hexagon of side 12 cm is inscribed in a circle. What is the length of the side of an equilateral triangle which is inscribed in the same circle?

A regular hexagon of side 12 cm is inscribed in a circle. What is the length of the side of an equilateral triangle which is inscribed in the same circle? Correct Answer 12√3 cm

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Suppose the length of side of triangle is x cm;

∴ Length of circumradius of the triangle = x/√3 cm

Since the hexagon of side 12 cm is also inscribed in the circle;

∴ Radius of the circle = 12 cm

∴ x/√3 = 12

⇒ x = 12√3

∴ Length of the side of a triangle = 12√3 cm

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