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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