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`.
Promotional Banner

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

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.

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 ?

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

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

CENGAGE-TRIGONOMETRIC FUNCTIONS-Solved Examples And Exercises
  1. If in a triangleA B C , (2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a) ...

    Text Solution

    |

  2. If the angles of a triangle are 30^0a n d45^0 and the included side is...

    Text Solution

    |

  3. A circle is inscribed in an equilateral triangle of side adot The area...

    Text Solution

    |

  4. In triangle A B C ,A D is the altitude from Adot If b > c ,/C=23^0,a n...

    Text Solution

    |

  5. If D is the mid-point of the side B C of triangle A B C and A D is per...

    Text Solution

    |

  6. In A B C ,A(2pi)/3,b-c=3sqrt(3)c m and area of A B C=(9sqrt(3))/2c m...

    Text Solution

    |

  7. The general value of theta satisfying the equation tan^2theta+sec2thet...

    Text Solution

    |

  8. In any triangle A B C ,(a^2+b^2+c^2)/(R^2) has the maximum value of 3 ...

    Text Solution

    |

  9. Solve sqrt(5-2 sin x)=6 sin x-1

    Text Solution

    |

  10. In triangle A B C ,R(b+c)=asqrt(b c),w h e r eR is the circumradius o...

    Text Solution

    |

  11. Solve sin^3thetacostheta-cos^3thetasintheta=1/4dot

    Text Solution

    |

  12. In A B C ,P is an interior point such that /P A B=10^0/P B A=20^0,/P ...

    Text Solution

    |

  13. Solve 4costheta-3sectheta=tantheta

    Text Solution

    |

  14. In A B C , if A B=c is fixed, and cosA+cosB+2cos C=2 then the locus o...

    Text Solution

    |

  15. Solve the equation 2cos^2theta+3sintheta=0

    Text Solution

    |

  16. In A B C , if b^2+c^2=2a^2, then value of (cotA)/(cotB+cotC) is 1/2 ...

    Text Solution

    |

  17. Find the number of solution of [cosx]+|sinx|=1, x inpilt=xlt=3pi (whe...

    Text Solution

    |

  18. If sinthetaa n d-costheta are the roots of the equation a x^2-b x-c=0 ...

    Text Solution

    |

  19. If the equation asinx+cos2x=2a-7 possesses a solution, then find the ...

    Text Solution

    |

  20. In A B C ,(a+b+c)(b+c-a)=k b c if k<0 (b) k >0 =<k<4 (d) k >4

    Text Solution

    |