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

a)sec(π/9)

b)cosec(π/9)

c)sin(π/9)

d)tan(π/9)

Dear student 

Here is another method.
Let AB=2 unit be one of the sides of the polygon.
Angle AOB = 2pi/9 
O is centre of circle 
OL is perpendicular to AB and AL = 1 and angle AOL = pi/9 
Radius of circle = OA = cscpi/9