Home
Class 10
MATHS
In equilateral DeltaABC, D is a point on...

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

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    KUMAR PRAKASHAN|Exercise OBJECTIVE QUESTIONS|37 Videos

  • TRIANGLES

    KUMAR PRAKASHAN|Exercise TEST YOUR SKILLS|29 Videos

  • SURFACE AREAS AND VOLUMES

    KUMAR PRAKASHAN|Exercise TEST YOUR SKILLS|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 9AD^(2)= 7AB^(2) .

In an equilateral ABC, E is a point on BC such that BE= (1)/(4)BC . Prove that 16AE^(2)= 13AB^(2) .

ABC is a triangle with AB= AC and D is a point on AC such that BC^(2)= AC xx CD . Prove that BD= BC.

In the given figure, D is a point on side BC of DeltaABC such that (BD)/(CD)=(AB)/(AC) . Prove that AD is the bisector of /_BAC .

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

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

ABC is a triangle . D is a point of AB such that AD=(1)/(4)AB and E is a point on AC such that AE=(1)/(4)AC. If DE =2cm find BC.

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

In triangle ABC, AB gt AC and D is any point of BC. Prove that, AB gt AD.

KUMAR PRAKASHAN-TRIANGLES-PRACTICE THOROUGHLY
  1. In DeltaABC, D and E are points on the sides AB and AC respectively su...

    Text Solution

    |

  2. DeltaABC ~ DeltaPQR. If AB= 6.5 cm, PQ= 10.4 cm and the perimeter of D...

    Text Solution

    |

  3. In DeltaABC, D and E are points of sides AB and AC such that DE||BC. I...

    Text Solution

    |

  4. An aeroplane leaves an airport and flies due west at a speed of 2100 k...

    Text Solution

    |

  5. In the given figure, OA= 3cm, OB= 4 cm, /AOB= 90^(@), AC= 12 cm" and "...

    Text Solution

    |

  6. In trapezium ABCD, AB||CD and AB= (1)/(3)CD. The diagonals AC and BD i...

    Text Solution

    |

  7. DeltaABC" and "DeltaDEF are two equilateral triangles of sides 4 cm an...

    Text Solution

    |

  8. A girl of height 100 cm is walking away from the base of a lamp-post a...

    Text Solution

    |

  9. In triangleABC, /C= 90^(@) and P and Q are the midpoints of BC and AC ...

    Text Solution

    |

  10. In the given figure, /B= 90^(@). If AE= CD= 13 cm and BE= AD= 5 cm, th...

    Text Solution

    |

  11. In the given figure, EFGD is a square and /BAC= 90^(@). Prove that BF ...

    Text Solution

    |

  12. In right angled DeltaABC, /C= 90^(@) and D, E, F are three points on B...

    Text Solution

    |

  13. In an equilateral ABC, E is a point on BC such that BE= (1)/(4)BC. Pro...

    Text Solution

    |

  14. A rhombus has each side of length 20 cm and one pair of opposite angle...

    Text Solution

    |

  15. In DeltaABC, /B=90^(@). D and E are any points on sides AB and BC resp...

    Text Solution

    |

  16. In DeltaABC, /B= 90^(@) and BM is an altitude. Prove that (1)/(BM^2)= ...

    Text Solution

    |

  17. ABCD is a rhombus. Prove that AB^(2)+BC^(2)+CD^(2)+DA^(2)= AC^(2)+BD^(...

    Text Solution

    |

  18. In equilateral DeltaABC, D is a point on BC such that BD= (1)/(3)BC. P...

    Text Solution

    |

  19. If A be the area of a right Deltaand b be one of the sides containing ...

    Text Solution

    |

  20. The perimeter of a right triangle 60 cm. If its hypotenuse is 25 cm, f...

    Text Solution

    |