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For a regular polygon, let r and R be th...

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is There is a regular polygon with `r/R=1/(sqrt(2))` (17) There is a regular polygon with `r/R=2/3` (30) There is a regular polygon with `r/R=(sqrt(3))/2` (47) There is a regular polygon with `r/R=1/2` (60)

A

There is a regular polygon with `(r)/(R) = (sqrt3)/(2)`

B

There is a regular polygon with `(r)/(R) = (1)/(2)`

C

There is a regular polygon with `(r)/(R) = (1)/(sqrt2)`

D

There is a regular polygon with `(r)/(R) = (2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`r = (a)/(2) "cot"(pi)/(n) and R = (a)/(2) "cosec"(pi)/(n)`
`:. (r)/(R) = ("cot"(pi)/(n))/("cosec"(pi)/(n)) = "cos"(pi)/(n)`

`:. "cos" (pi)/(n) != (2)/(3) " for any " n in N`
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