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

In an equilateral triangle ABC, D is a point on side BC such that `B D=1/3B C`. Prove that `9A D^2=7A B^2`.

Text Solution

Verified by Experts

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

Topper's Solved these Questions

  • TRIANGLES

    MTG IIT JEE FOUNDATION|Exercise NCERT Section Exercise 6 .6|12 Videos
  • TRIANGLES

    MTG IIT JEE FOUNDATION|Exercise Exercise (Multiple Choice Questions) (LEVEL -1 ) |35 Videos
  • TRIANGLES

    MTG IIT JEE FOUNDATION|Exercise NCERT Section Exercise 6.4|9 Videos
  • SURFACE AREAS AND VOLUMES

    MTG IIT JEE FOUNDATION|Exercise OLYMPIAD/HOTS CORNER|20 Videos

Similar Questions

Explore conceptually related problems

The perimeters of two similar triangles are 25cm and 15cm respectively. If one side of the first triangle is 9cm, find the length of the corresponding side of the second triangle. OR 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)

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

DeltaABC is an equilateral triangle. Point D is on side BC such that BD=(1)/(5)BC then prove 25AD^(2)=21AB^(2) .

In an equilateral triangle ABC the side BC is trisected at D. Prove that 9AD^(2)=7AB^(2)

In a scalene triangle A B C ,D is a point on the side A B such that C D^2=A D D B , sin s in A S in B=sin^2C/2 then prove that CD is internal bisector of /_Cdot

In an equilateral triangle ABC, the side BC is trisected at D. Then the correct relation is

A point D is on the side BC of an equilateral triangle ABC such that DC=(1)/(4)BC. Prove that AD^(2)=13CD^(2)

In a triangle ABC, D is midpoint of side BC. If ACgtAB and AE_|_BC , then prove that AB^(2)=AD^(2)-BC.ED+(1)/(4)BC^(2)

MTG IIT JEE FOUNDATION-TRIANGLES -NCERT Section Exercise 6.5
  1. Sides of triangle are given below. Determine which of them are right t...

    Text Solution

    |

  2. Sides of triangles are given below. Determine which of them right t...

    Text Solution

    |

  3. Sides of triangle are given below .Determine which of them are rig...

    Text Solution

    |

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

    Text Solution

    |

  5. In Figure 2, Delta ABD is a right triangle, right-angled at A and AC |...

    Text Solution

    |

  6. In the figure , ABD is a triangle right angled at A and AC bot Bd . Sh...

    Text Solution

    |

  7. ABC is an isosceles triangle right angled at C. Prove that A B^2=2A C...

    Text Solution

    |

  8. ABC is an isosceles triangle with AC = BC. If A B^2=2A C^2, prove tha...

    Text Solution

    |

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

    Text Solution

    |

  10. Prove that the sum of the squares of the sides of a rhombus is equa...

    Text Solution

    |

  11. In figure, O is a point in the interior of a triangle ABC, O D|B C ,O...

    Text Solution

    |

  12. A ladder 10m long reaches a window 8 m above the ground. Find the d...

    Text Solution

    |

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

    Text Solution

    |

  14. An aeroplane leaves an airport and flies due north at a speed of 1000...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  17. The perpendicular from A on side BC of a ABC intersects BC at D such t...

    Text Solution

    |

  18. In an equilateral triangle ABC, D is a point on side BC such that B D=...

    Text Solution

    |

  19. In an equilateral triangle, prove that three times the square of on...

    Text Solution

    |

  20. Tick the correct answer and justify: In DeltaA B CdotAB = 6sqrt(3)cm...

    Text Solution

    |