Question

For a regular hexagon of perimeter 18 cm inscribed in a circle, the radius of the circle is ______.

Options

• 6 cm

• 9 cm

• 3 cm

• none of these

Answer 1

For a regular hexagon of perimeter 18 cm inscribed in a circle, the radius of the circle is 3 cm.

Explanation:

We know that,

A regular hexagon comprises 6 equilateral triangles.

∴ BAC is an equilateral triangle.

∴ AB = BC = CA.

From figure,

AB and AC are radius of the circle.

In a regular hexagon, length of each side is equal.

Thus,

BC = `18/6​` = 3 cm.

∴ AB = AC = 3 cm

Thus, radius of circle = 3 cm.