Home
Class 10
MATHS
In an equilateral triangle ABC , D is a ...

In an equilateral triangle ABC , D is a point on side BC such that BD = `1/3` BC . Prove that `9 AD^(2)=7AB^(2)` .

Text Solution

Verified by Experts

The correct Answer is:
`9 AD^(2) = 7 AB^(2) ` (proved)
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    CPC CAMBRIDGE PUBLICATION|Exercise Exercise 2.6 (Optional)|8 Videos
  • TRIANGLES

    CPC CAMBRIDGE PUBLICATION|Exercise Exercise 2.4|9 Videos
  • SURFACE AREAS AND VOLUMES

    CPC CAMBRIDGE PUBLICATION|Exercise EXERCISE 15.4|5 Videos

Similar Questions

Explore conceptually related problems

In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC . Prove that 9 AD^(2) = 7 AB^(2) .

In an equilateral triangle ABC, D is a point on side BC such that BD = (1)/(3) BC. Prove that 9 AD^(2) = 7 AB^(2) .

In an equilateral triangle ABC, D is a point of BC such that 4BD = BC. Prove that 16AD^(2)=13BC^(2) .

In an equilateral triangle ABC, AD is drawn perpendicular to BC meeting BC in A Prove that AD^(2) = x BD^(2) Find x.

D is a point on side BC ΔABC such that AD = AC (see figure). Show that AB > AD.

In Delta ABC , C is a point on BD such that BC:CD=1:2 and △ABC is an equilateral triangle Prove that AD^(2) = 7AC^(2)

In an equilateral triangle ABC, AD _|_ BC . Prove that : AB^(2) + CD^(2) = 5/4 AC^(2)

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD (see figure) Show that AD = AE

In a triangle ABC, AD is the median drawn on the side BC is produced to E such that AD = ED prove that ABEC is a parallelogram.

The perpendicular from A on side BC of a DeltaABC intersects BC at D such the DB = 3 CD . Prove that 2 AB^(2)=2AC^(2)+BC^(2)

CPC CAMBRIDGE PUBLICATION-TRIANGLES-Exercise 2.5
  1. Sides of triangles are given below. Determine which of them are right ...

    Text Solution

    |

  2. PQR is a triangle right angled at P and M is a point on QR such that P...

    Text Solution

    |

  3. In Fig. ABD is a triangle right angled at A and AC bot BD show that ...

    Text Solution

    |

  4. ABC is an isosceles triangle right angled at C . Prove that AB^(2)=2A...

    Text Solution

    |

  5. ABC is an isosceles triangle with AC=BC . If AB^(2)=2AC^(2) , prove t...

    Text Solution

    |

  6. ABC is an equilateral of side 2a . Find each of its altitudes.

    Text Solution

    |

  7. Prove that sum of the squares of the side of a rhombus is equal to th...

    Text Solution

    |

  8. In fig . O is a point in the interior of a triangle ABC , OD bot BC ,...

    Text Solution

    |

  9. A ladder 10 m long reaches a window 8 m above the ground. Find the di...

    Text Solution

    |

  10. A guy wire attached to a vertical pole of height 18 m is 24 m long and...

    Text Solution

    |

  11. A stone is dropped from a height of 100 m and at the same time another...

    Text Solution

    |

  12. Two poles of heights 6 m and 11 m stand on a plane ground. If the di...

    Text Solution

    |

  13. D and E are points on the sides CA and CB respectively of a triangle A...

    Text Solution

    |

  14. The perpendicular from A on side BC of a DeltaABC intersects BC at D...

    Text Solution

    |

  15. In an equilateral triangle ABC , D is a point on side BC such that BD ...

    Text Solution

    |

  16. In an equilateral triangle , prove that three times the square pf one ...

    Text Solution

    |

  17. In Delta ABC ,AB = 6 sqrt(3) cm AC = 12 cm and BC = 6 cm . The an...

    Text Solution

    |