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A circle is inscribed in an equilateral ...

A circle is inscribed in an equilateral triangle of side `adot` The area of any square inscribed in this circle is ______.

Text Solution

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The correct Answer is:
`(a^(2))/(6)`sq unit
In an equilateral triangle, the radius of incircle
`=(1)/(3)xx` median of the triangle
`=(1)/(3)sqrt(a^(2)-(a^(2))/(4))=(1)/(3)sqrt((4a^(2)-a^(2))/(4))=(a)/(2sqrt3)`
therefore ,area of the square inscribed in this circle
`=2("radius of circle")^(2) = (2a^(2))/(4*3)= (a^(2))/(6)` sq unit
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Knowledge Check

  • A circle is inscribed in an equilateral triangle of side a. What is the area of any square inscribed in the circle ?

    A
    `(a^(2))/(3)`
    B
    `(a^(2))/(4)`
    C
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    D
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  • A circle is cirumscribed in an equilateral triangle of side 'l' . The area of any square inscribed in the circle is :

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    B
    `(2)/(3)l^(2)`
    C
    `(1)/(3)l^(2)`
    D
    `l^(2)`

  • A circle is inscribed in a equilateral triangle of side 24 cm. What is the area ( in cm^(2) ) of a square inscribed in the circle ?

    A
    48
    B
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