Home
Class 12
MATHS
In A B C , A D is a median. Prove th...

In ` A B C` , `A D` is a median. Prove that `A B^2+A C^2=2\ A D^2+2\ D C^2` .

Promotional Banner

Topper's Solved these Questions

  • RELATIONS

    RD SHARMA ENGLISH|Exercise All Questions|197 Videos
  • SCALAR TRIPLE PRODUCT

    RD SHARMA ENGLISH|Exercise All Questions|76 Videos

Similar Questions

Explore conceptually related problems

A B C D is a rhombus. Prove that A B^2+B C^2+C D^2+D A^2=A C^2+B D^2

A B C is a triangle in which A B=A C and D is any point in B C . Prove that A B^2-A D^2=B D C D .

In A B C , A D is perpendicular to B C . Prove that: A B^2+C D^2=A C^2+B D^2 (ii) A B^2-B D^2=A C^2-C D^2

If A D is the median of A B C , using vectors, prove that A B^2+A C^2=2(A D^2+C D^2)dot

The perpendicular A D on the base B C of a triangle A B C intersects B C at D so that D B=3C D . Prove that 2\ A B^2=2\ A C^2+B C^2 .

In a quadrilateral A B C D , given that /_A+/_D=90o . Prove that A C^2+B D^2=A D^2+B C^2 .

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

In /_\ A B C , given that A B=A C and B D_|_A C . Prove that B C^2=2\ A C * C D

In an equilateral A B C , A D_|_B C , prove that A D^2=3\ B D^2

RD SHARMA ENGLISH-SCALAR OR DOT PRODUCT-All Questions
  1. Using analytical geometry, prove that the diagonals of a rhombus are ...

    Text Solution

    |

  2. Prove that the diagonals of a rectangle are perpendicular if and on...

    Text Solution

    |

  3. In A B C , A D is a median. Prove that A B^2+A C^2=2\ A D^2+2\ D C...

    Text Solution

    |

  4. If the median to the base of a triangle is perpendicular to the bas...

    Text Solution

    |

  5. In a quadrilateral A B C D , prove that A B^2+B C^2+C D^2+D A^2=A C^2+...

    Text Solution

    |

  6. What is the angle between vectors vec a\ a n d\ vec b with magnitude...

    Text Solution

    |

  7. If vec a\ a n d\ vec b are two vectors such that vec adot vec b=6,\...

    Text Solution

    |

  8. Find the cosine of the angle between the vectors 4 hat i-3 hat j+3 hat...

    Text Solution

    |

  9. If the vectors 3 hat i+m hat j+ hat k\ a n d\ 2 hat i- hat j-8 hat k a...

    Text Solution

    |

  10. If the vectors 3 hat i-2 hat j-4 hat k\ a n d\ 18 hat i-12 hat j-m hat...

    Text Solution

    |

  11. If vec a\ a n d\ vec b are vectors of equal magnitude, write the val...

    Text Solution

    |

  12. If vec a\ a n d\ vec b are two vectors such that ( vec a+ vec b)dot(...

    Text Solution

    |

  13. For any two vectors vec a\ a n d\ vec b write when | vec a+ vec b|=|...

    Text Solution

    |

  14. For any two vectors vec a\ a n d\ vec b write then | vec a+ vec b|=|...

    Text Solution

    |

  15. If vec a\ a n d\ vec b are two vectors of the same magnitude incline...

    Text Solution

    |

  16. If vec adot vec adot=0\ a n d\ vec adot vec b=0 what can you conclud...

    Text Solution

    |

  17. If vec b is a unit vector such that ( vec a+ vec b)dot ( (vec a- vec ...

    Text Solution

    |

  18. If hat a ,\ hat b are unit vector such that\ hat a+ hat b is a unit...

    Text Solution

    |

  19. If | vec a|=13 ,\ | vec b|=5\ a n d\ vec adot vec b=60 , t h e n find...

    Text Solution

    |

  20. If vec a= hat i- hat j\ a n d\ vec b=- hat j+ hat k find the project...

    Text Solution

    |