Question

A regular hexagon is inscribed in circle of radius r. The perimeter of regular hexagon is

• A. 3r
• B. 6r
• C. 9r
• D. 12r

Answer 1

The correct option is B 6r

The regular hexagon is inscribed in a circle of radius $r$.

So, it is inside the circle.

By joining opposite sides of hexagon, it forms $6$ central angles at centre $O$ each of which $=\frac{360}{6}={60}^o$.

And the six triangles are formed.

The two sides of each triangle are the radius of the circle and thus are equal., $\therefore$ The base angles of every triangle are equal.

$\because$ Central angle is ${60}^o$

$⟹$ Base angles $=120/2={60}^o$

$\therefore$ The triangles are equilateral triangles.

$⟹$ All sides are equal.

$\therefore$ All sides of each triangle is $r$

Perimeter of regular hexagon $=6\times side=6r$
Hence, option B is correct.