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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)

Text Solution

Verified by Experts

`cos pi/n = r/R`
`n=1; r/R= -1`
`n=2 ; r/R=0`
`n=3 ; r/R=1/2`
`n=4 ; r/R = 1/sqrt2`
`n=5 ; r/R= cos 36^@`
`n=6 ; r/R = sqrt3/2`
option 2 is correct
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