Home
Class 10
MATHS
∆PQR is right angled at Q and the points...

`∆PQR` is right angled at Q and the points S and T trisect the side QR. Prove that `8PT^2 = 3PR^2 + 5PS^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

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

PQR is a triangle right angled at P and M is a point on QR such that PM_|_QR .Show that PM^2=QM.MR .

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

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

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

Prove that log_3 log_2 8=1

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 .

ABC is a right angled triangle right angled at C. CD is perpendicular on the hypotenuse AB. Prove that (AC^2)/(BC^2)=(AD)/(DB)

ABC is a right angled triangle right angled at C. CD is perpendicular on the hypotenuse AB. Prove that (BC^2)/(CD^2)=(AB)/(AD)

KALYANI PUBLICATION-PYTHAGORAS THEOREM-EXERCISE
  1. ∆ABC is a right angled triangle right angled at A and AD | BC. Prove t...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  13. Prove that the sum of the squares of the sides of a rhombus is equal t...

    Text Solution

    |

  14. A ship rail 25 km due south and then 60 km due west. How far it is the...

    Text Solution

    |

  15. B is due west of A and C is due north of B. If the distance between B ...

    Text Solution

    |

  16. A man travels 27 km due south then 24 km due west. Finally 20 km due n...

    Text Solution

    |

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

    Text Solution

    |

  18. In an isosceles triangle ABC if AC=BC and AB^2 = 2AC^2, prove that /C ...

    Text Solution

    |

  19. The length of the sides of a triangle are ax-by,ay+bx and sqrt((a^2+b^...

    Text Solution

    |

  20. The length of the sides of a triangle are a+b,ab-1 and sqrt((a^2+1)(b^...

    Text Solution

    |