Question

# A regular polygon of nine sides, each of length 2 is inscribed in a circle. The radius of the circle is -

Hint:

### A regular polygon of nine sides, each of length 2 is inscribed in a circle. We have find the radius of the circle. Here a nine side polygon inscribe in it.

## The correct answer is:

### Here we have to find that radius of the circle.

Firstly,

There are nine side of polynomial inscribe, so angle for 1 side,

Central angle is = = 40°

So angle ∠ACB = 40°

⊥CM on AB ,

∠ACM = = 20° [ CM is perpendicular bisector]

AB is side of polynomial of 2 unit then AM = MB = 1unit

CA is also a radius so let CA be r.

In △AMC,

Sin 20° =

Sin 20°= [ since AM = r and CA = r]

r =

r = cosec 20°

The radius of circle = cosec ()

Therefore, the correct answer is cosec ().

In this question, we have to find the radius of circle, In nine sided polygon is given , angle of 1 side is 40°. And also the all sides of polynomial are equals.

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