Home
Class 12
MATHS
Let 'l' is the length of medians from th...

Let 'l' is the length of medians from the vertex A to the side BC of a `DeltaABC,` then

A

`4l^(2)=2b^(2)+2c^(2)-a^(2)`

B

`4l^(2)=b^(2)+c^(2) +2bc cos A`

C

`4l^(2)=b^(2)+4bc cos A `

D

`4l^(2)- (2s-a)^(2) -4 bc sin ^(2)((A)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Promotional Banner

Topper's Solved these Questions

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|15 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|25 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|65 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|52 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

Similar Questions

Explore conceptually related problems

Let 'l' is the length of median from the vertex A to the side BC of a Delta ABC . Then

In Delta ABC, 'h' is the length of altitude drawn from vertex A on the side BC. Prove that: 2(b^(2) +c^(2)) ge 4h^(2) +a^(2). Also, discuss the case when equality holds true.

Find the length of the perpendicular from the vertex B of triangle ABC to the median through C if A is (-10, -13), B is (-2, 3) and C is (2,1).

The lengths of the sides of a triangle are 4 cm, 12 cm and 13 cm. Find the length of the perpendicular form the opposite vertex to the side whose length is 13 cm

Let position vectors of point A,B and C of triangle ABC represents be hati+hatj+2hatk, hati+2hatj+hatk and 2hati+hatj+hatk . Let l_(1),l_(2) and l_(3) be the length of perpendicular drawn from the orthocenter 'O' on the sides AB, BC and CA, then (l_(1)+l_(2)+l_(3)) equals

Find the area of a parallelogram. Also find the length of the altitude from vertex A on the side DC.

In a DeltaABC, B=90^(@), AC=h and the length of perpendicular from B to AC is p such that h=4p. If AB lt BC, then measure angleC.

ARIHANT MATHS-PROPERTIES AND SOLUTION OF TRIANGLES -Exercise (More Than One Correct Option Type Questions)
  1. Find the second order derivative of the function 2logx^2 + 4x

    Text Solution

    |

  2. Is it possible to have a DeltaABC with a=3,b=5, c=7 and C =(2pi)/(3) ...

    Text Solution

    |

  3. Find the second order derivative of the function x.cosx

    Text Solution

    |

  4. Differentiate the following w.r.t x (x + 3)^2 . (x + 4)^3

    Text Solution

    |

  5. Find the second order derivative of the function x^(6) + 2

    Text Solution

    |

  6. Given an isoceles triangle with equal side of length b and angle alpha...

    Text Solution

    |

  7. There can exist a triangle ABC satisfying the condition (sin A)/(2) =(...

    Text Solution

    |

  8. Find (d^2y)/dx^2 , if y = logx

    Text Solution

    |

  9. If in DeltaABC, A =90^(@) and c, sin B and cos B are rational number, ...

    Text Solution

    |

  10. Find second order derivative of the function sin^(-1)x

    Text Solution

    |

  11. Let 'l' is the length of medians from the vertex A to the side BC of a...

    Text Solution

    |

  12. If A,A1,A2 and A3 are the areas of the inscribed and escribed circles ...

    Text Solution

    |

  13. If a, b, A be given in a triangle and c1 and c2 be two possible value ...

    Text Solution

    |

  14. D,E and F are the middle points of the sides of the triangle ABC, then

    Text Solution

    |

  15. The sides of A B C satisfy the equation 2a^2+4b^2+c^2=4a b+2ac Then a...

    Text Solution

    |

  16. If Delta represents the area of acute angled triangle ABC, then sqrt(a...

    Text Solution

    |

  17. In triangle, A B Cif2a^2b^2+2b^2c^2=a^2+b^4+c^4, then angle B is equal...

    Text Solution

    |

  18. If H is the orthocentre of triangle ABC, R = circumradius and P = AH +...

    Text Solution

    |

  19. If inside a big circle exactly n(nlt=3) small circles, each of radius ...

    Text Solution

    |

  20. If in triangle ABC, a, c and angle A are given and c sin A lt a lt c, ...

    Text Solution

    |