Question

Question No: 6
Which of the following is equal to the radius of the circle if the octagon is a regular octagon?
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Answer 1

Answer:

The radius of circle is 1

The angle between adjacent sides of regular octagon is (8−2)180/8=135

The angle made by each side at center is 360/8=45

Let the side length of regular octagon be a

By sine rule , we get a/sin45=1/sin(62.5) , which implies a=sin45/sin(62.5)=

2−

2

Answer 2

Answer: $\sqrt{2-\sqrt{2} }$

Step-by-step explanation: As we know, the radius of the circle is 1,

Now the angle between adjacent sides of a regular octagon is $(8-2)\frac{180}{8} =6*\frac{180}{8}=\frac{1080}{8} =135$

So now the angle made by each side at the center is $\frac{360}{8}=45$

Let the side length of a regular octagon be a

Now, by the use of the sine rule,

we get $\frac{a}{sin45}=\frac{1}{sin(62.5)}$

As which implies $a=\frac{sin 45}{sin 62.5} =\sqrt{2-\sqrt{2} }$

Hence,  the$\sqrt{2-\sqrt{2} }$ is equal to the radius of the circle if the octagon is a regular octagon.

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