Home
Class 10
MATHS
If PB and AQ are the medians of a ∆ABC r...

If PB and AQ are the medians of a `∆ABC` right angled at C. Prove that
`4AQ^2 = 4 AC^2 + BC^2`

Promotional Banner

Topper's Solved these Questions

  • PYTHAGORAS THEOREM

    KALYANI PUBLICATION|Exercise EXERCISE|48 Videos

  • PROBABILITY

    KALYANI PUBLICATION|Exercise EXERCISE|63 Videos

  • QUADRATIC EQUATION

    KALYANI PUBLICATION|Exercise EXERCISE|144 Videos

Similar Questions

Explore conceptually related problems

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4BP^2 = 4 BC^2 + AC^2

If PB and AQ are the medians of a ∆ABC right angled at C. Prove that 4 (AQ^2 + BP^2) = 5 AB^2

P and Q are points on the sides CA and CB of a ∆ABC , right angled at C. Prove that AQ^2 + BP^2 = AB^2 + PQ^2 .

If x and y are the mid-points of the sides CA and CB respectively of a ∆ABC right angled at C. prove that 4Ay^2=4AC^2 +BC^2

ABC is an isosceles triangle right angled at C.Prove that AB^2=2AC^2 .

D and E are points on the sides CA and CB respectively of a triangle ABC right angled at C.Prove that, AE^2+BD^2=AB^2+DE^2 .

∆ABC is a right angled at B and D is mid-point of BC. Prove that AC^2 = 4AD^2 - 3AB^2 .

If D is the middle point of the side BC of the triangle ABC, prove that AB^2 + AC^2 = 2(AD^2 + DC^2) .

∆ABC is a right angled triangle right angled at A and AD _|_ BC . Prove that AD^2 = BD.CD .

In Fig.6.60, AD is a median of a triangle ABC and AM_|_BC .Prove that :(i) AC^2=AD^2+BC.DM+((BC)/2)^2

KALYANI PUBLICATION-PYTHAGORAS THEOREM-EXERCISE
  1. ABC is an isosceles triangle right angled at C.Prove thatAB^2=2AC^2.

    Text Solution

    |

  2. If x and y are the mid-points of the sides CA and CB respectively of ...

    Text Solution

    |

  3. If PB and AQ are the medians of a ∆ABC right angled at C. Prove that ...

    Text Solution

    |

  4. If PB and AQ are the medians of a ∆ABC right angled at C. Prove that ...

    Text Solution

    |

  5. If PB and AQ are the medians of a ∆ABC right angled at C. Prove that ...

    Text Solution

    |

  6. ABC a right angle triangle, right angled at B. AD and CE are the media...

    Text Solution

    |

  7. P and Q are points on the sides CA and CB of a ∆ABC , right angled at...

    Text Solution

    |

  8. In ∆ABC , AD | BC such that AD^2 = BD.CD. Prove that ∆ABC is right ang...

    Text Solution

    |

  9. ∆ABC is a right angled triangle right angled at A and AD | BC. Prove t...

    Text Solution

    |

  10. ∆ABC is a right angled at B and D is mid-point of BC. Prove that AC^2 ...

    Text Solution

    |

  11. ∆PQR is right angled at Q and the points S and T trisect the side QR. ...

    Text Solution

    |

  12. In an equilateral triangle, prove that three times the square of one s...

    Text Solution

    |

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

    Text Solution

    |

  14. ∆ABC is right angled at C and CD | AB. If BC = a , CA=b , AB = c and C...

    Text Solution

    |

  15. Of triangle ABC,angleB=90^@ and BD|AC.IF AB=c,BC=a,CA=b and BD=p then ...

    Text Solution

    |

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

    Text Solution

    |

  17. Two poles of height 10 m and 15 m stand vertically on a plane ground. ...

    Text Solution

    |

  18. In Fig.6.45,O is a point in the interior of a triangle ABC,OD|BC,OE|AC...

    Text Solution

    |

  19. O is a point in the interior of ∆ABC. OD,OE and OF are the perpendicul...

    Text Solution

    |

  20. O is any point inside a rectangle ABCD. Prove that OB^2+OD^2=OA^2+OC^2...

    Text Solution

    |