Home
Class 11
MATHS
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

Verified by Experts

`tan30=r/(a/2)`
`r=(a/(2sqrt3))`
Side of square=`2(rsin45)`
`=2*(a/(2sqrt3*sqrt2))`
`a'=a/sqrt6`
Area of square=`a^2/6`.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • STRAIGHT LINES

    CENGAGE|Exercise Solved Examples And Exercises|482 Videos

Similar Questions

Explore conceptually related problems

A circle is inscribed in an equilateral triangle of side a. Find the area of any square inscribed in this circle.

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

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
    `(a^(2))/(6)`
    D
    `(a^(2))/(8)`

  • A circle is cirumscribed in an equilateral triangle of side 'l' . The area of any square inscribed in the circle is :

    A
    `(4)/(3)l^(2)`
    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
    72
    C
    54
    D
    96

    • Similar Questions

    Explore conceptually related problems

    A circle is inscribed in an equilateral triangle of side a. The area of any square inscribed in this circle is (A) a^2/12 (B) a^2/6 (C) a^2/3 (D) 2a^2

    A square inscribed in a circles.

    The area of a square inscribed in a circle of radius 8 cm is:

    The area of circle inscribed in an equilateral triangle of side 12 cm is

    The area of circle inscribed in an equilateral triangle of side 12 cm is

    Home
    Profile