Home
Class 12
MATHS
Prove that the least perimeter of an iso...

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is `6sqrt3r`.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

An isosceles triangle with base 24 and legs 15 each is inscribed in a circle . Find the radius

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

The base vertices of an isosceles triangle PQR are Q (1,3) and R(-2, 7). The vertex P can be-

The maximum area of a rectangle that can be inscribed in a circle of radius 2 unit is (in sq unit)

ABCD be a cycle quadrilateral inscribed in a circle of radius R. The sides of a quadrilateral which can be inscribed in a circle are 6,6,8and 8cm.Then radius of circumcircle is

Show that of all isosceles triangles inscribed in a given circle, the equilateral triangle has the greatest area.

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

Find the dimensions of the rectangle of maximum perimeter that can be inscribed in a circle of radius a.

Find the volume of the largest cylinder inscribed in the sphere of radius r cm.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. If f(x)=x+sinx ,g(x)=e^(-x),u=sqrt(c+1)-sqrt(c), v=sqrt(c) -sqrt(c-1...

    Text Solution

    |

  2. The length of the largest continuous interval in which the function f(...

    Text Solution

    |

  3. Prove that the least perimeter of an isosceles triangle in which a cir...

    Text Solution

    |

  4. A given right cone has volume p , and the largest right circular cylin...

    Text Solution

    |

  5. The function f(x)=x^(1/3)(x-1) has two inflection points, has one poi...

    Text Solution

    |

  6. Tangents are drawn to x^2+y^2=16 from the point P(0, h)dot These tange...

    Text Solution

    |

  7. The largest area of the trapezium inscribed in a semi-circle or radius...

    Text Solution

    |

  8. A bell tent consists of a conical portion above a cylindrical portion ...

    Text Solution

    |

  9. A rectangle is inscribed in an equilateral triangle of side length 2a ...

    Text Solution

    |

  10. The fuel charges for running a train are proportional to the square of...

    Text Solution

    |

  11. A cylindrical gas container is closed at the top and open at the botto...

    Text Solution

    |

  12. In a triangleA B C ,/B=90^0 and b+a=4. The area of the triangle is ma...

    Text Solution

    |

  13. The three sides of a trapezium are equal, each being 8cm. The area of ...

    Text Solution

    |

  14. A rectangle with one side lying along the x-axis is to be inscribed in...

    Text Solution

    |

  15. A right triangle is drawn in a semicircle of radius 1/2 with one of ...

    Text Solution

    |

  16. The least area of a circle circumscribing any right triangle of area 9...

    Text Solution

    |

  17. The least integral value of x where f(x)=(log)(1/2)(x^2-2x-3) is monot...

    Text Solution

    |

  18. L e tf(x)={x+2 , x <-1 ; x^2 , -1 lt= x < 1 and (x-2)^2 , ...

    Text Solution

    |

  19. Number of integral values of b for which the equation (x^3)/3-x=b has ...

    Text Solution

    |

  20. Let f(x)={x^(3/5),ifxlt=1and (x-2)^3,ifx >1 Then the number of c...

    Text Solution

    |