Question

The circumference if a circle is 7cm longer than the perimeter of a regular inscribed hexagon Find the circumference​

Answer 1

Step-by-step explanation:

Since ABCDEF is an inscribed regular hexagon.

So each interior angle of it ={(n-2)*180°}÷n

={ (6–2)* 180°}÷ 6 = 720° /6 = 120°

So, each angle will be bisected into 60° ( as each triangle is congruent to other)

As the central angle is equally divided into 6 angles each measuring 60°

This way each triangle is an equuilateral triangle.

So, in triangle OAB, OA = OB = AB = r , where r is the radius of the circle.

Now, PERIMETER of regular hexagon = 6r

As per the condition given ,

Circumference = 7 + 6r

2 pi r = 7+ 6r

=> 2 pi r - 6r = 7

=> 2*(22/7)* r -6r = 7

=> r{(44/7) -6} =7

=> r*(2/7) = 7

=> r= 49/2

Now, circumference = 2*pi*r

= 2*(22/7) * (49/2)

= 154 cm………ANS