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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 )= (1)/(2)`

B

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

C

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

D

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

Text Solution

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The correct Answer is:
C
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Knowledge Check

  • For a regular polygon, let r, R be the radii of the inscribed and circumscribed circles. There is no regular polygo with

    A
    `(r )/(R ) =(2)/(3)`
    B
    `(r )/(R )=(sqrt(3))/(2)`
    C
    `(r )/(R )=(1)/(2)`
    D
    `(r )/(R )=(1)/(sqrt(2 ))`

  • For a regular polygon let r and R be radii of the inscribed and the circumscribed circles. Which one of the following is not true?

    A
    there is a regular polygon with `r/R =1/2`
    B
    there is a regular polygon with `r/R=sqrt3/2`
    C
    there is a regular polygon with `r/R = 2/3`
    D
    there is a regular polygon with `r/R =1/sqrt2`

  • The interior angle of a regular polygon with n sides is 6 times that of an exterior angle of a regular polygon with (3)/(2) n sides. Then n equals

    A
    12
    B
    20
    C
    10
    D
    18

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