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Regular pentagons are inscribed in two c...

Regular pentagons are inscribed in two circles of radius `5 `and `2` units respectively. The ratio of their areas is

Text Solution

Verified by Experts

The correct Answer is:
`25 : 4`
`Delta_(1) = (5R_(1)^(2))/(2) sin 72^(@)`
`Delta_(2) = (5R_(2)^(2))/(2) sin 72^(@)`
`rArr (Delta_(1))/(Delta_(2)) = (25)/(4)`
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Knowledge Check

  • The area of the triangle inscribed in a circle of radius 4 and the ratio of its angles in the ratio 5:4:3 is

    A
    `4(3+sqrt3)`
    B
    `4(sqrt3+sqrt2)`
    C
    `4(3-sqrt3)`
    D
    `4(sqrt3-sqrt2)`

  • If a regular hexagon is inscribed in a circle of radius 4 cm, then find the area of the polygon in cm^2

    A
    `6sqrt3`
    B
    `24sqrt3`
    C
    `4sqrt3`
    D
    `48sqrt3`

  • Let A_0A_1A_2A_3A_4A_5 be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments A_0A_1 , A_0A_2 and A_0A_4 is

    A
    44289
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