Question

If the vertices of regular hexagon having perimeter 60 cm are on the circumference of a circle . Find the radius of the circle.

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Answer 1

Given :

• Perimeter of the hexagon = 60 cm.

To find :

• Radius of the circle .

Solution :

Each chord ' x ' will make an angel ' ∅ ' at the centre of the circle.

Therefore,

6∅ = 360°

→ ∅ = 360°/6

→ ∅ = 60°

∆ AOB is a Equilateral triangle.

In case of ∆ AOB ,

$\sf{\angle\:AOB=60^\degree}$

So,

$\sf{\angle\:OAB=\angle\:OBA=60^\degree}$

Therefore ,

OA = OB

Perimeter of the hexagon = 60 cm.

A/Q,

6x = 60

→ x = 10

So,

AB = 10 cm

We know,

AB = OA = OB

Therefore , OA = OB = 10 cm.

Hence , the radius of the circle is 10 cm.