The ratio of the area of a regular polygon of `n` sides inscribed in a circle to that of the polygon of same number of sides circumscribing the same is 3:4. Then the value of `n` is 6 (b) 4 (c) 8 (d) 12

Options

A. 6
B. 4
C. 8
D. 12

Answer

A

Explanation

Let a be the radius of the circle, then the ratio of the area of regular polygons of n sides inscribed to circumscrbing the same circle is given by
`(S_(1))/(S_(2)) = ((1)/(2) na^(2) sin (2pi//n))/(na^(2) tan (pi//n)) = (3)/(4)`
`rArr cos^(2) ((pi)/(n)) = (3)/(4)`
or `cos ((pi)/(n)) = (sqrt3)/(2)`
or `(pi)/(n) = (pi)/(6) rArr n = 6`