Home
Class 10
MATHS
O is a point inside the trianglePQR and ...

O is a point inside the `trianglePQR` and frm O,OA,OB,OC are perpendicular one QR,RP and PQ. Prove that `PC^2+QA^2+RB^2 = PB^2+RA^2+QC^2`.

Promotional Banner

Topper's Solved these Questions

  • KANACHI HIGH SCHOOL

    UNITED BOOK HOUSE|Exercise EXERCISE|55 Videos
  • Partnership Business

    UNITED BOOK HOUSE|Exercise Exercise |30 Videos

Similar Questions

Explore conceptually related problems

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

In a triangle PQR, anglePQR = 90^@ S is any point onQR. Prove that PS^2+QR^2 = PR^2+QS^2 .

O is an internal point of the rectangle PQRS. Prove that OQ^(2)+OS^(2) = OP^(2) +QR^(2)

In a right angled traingle PQR , angleP is right angle and PS is perpendicular to the hypetnuse QR. Prove that 1/(PS^2)-1/(PQ^2)=1/(PR^2)

In a right-angled trigangle /_A is a right-angle and AO is perpendicular to BC at the point O . Prove that AO^(2)=BOxxCO .

PQR is a triangle whose /_Q is right angle. If S is any point on QR, then prove that PS^(2) + QR^(2) =PR^(2) + QS^(2)

‘O’ is any point inside a rectangle ABCD. Prove that OB^(2) + OD^(2) = OA^(2) + OC^(2)

‘O’ is any point in the interior of a triangle ABC. If OD bot BC, OE bot AC and OF bot AB, show that (i) OA^(2) + OB^(2) + OC^(2) - OD^(2) - OE^(2) - OF^(2) = AF^(2) + BD^(2) + CE^(2) (ii) AF^(2) + BD^(2) + CE^(2) = AE^(2) + CD^(2) + BE^(2) .

O is any point inside a rectangle ABCD, Prove that OA^(2) + OC^(2)= OB^(2) + OD^(2)

O is the centre of a centre having diameter AB. P is any point on the circle. Draw a perpendicular from P to AB, which meets AB at N. Prove that PB^2 =AB.BN

UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. Two tangents AB and AC drawn from an external point A of a circle touc...

    Text Solution

    |

  2. Does the point (–2.5, 3.5) lie inside, outside or on the circle x^2 + ...

    Text Solution

    |

  3. O is a point inside the trianglePQR and frm O,OA,OB,OC are perpendicul...

    Text Solution

    |

  4. ABCD is a cyclic quadrilaterla. Extended AB and DC intersect at P. Pr...

    Text Solution

    |

  5. A straight line L interesect the sides BC, CA and BA of triangleABC at...

    Text Solution

    |

  6. In a right angled traingle PQR ,angleP is right angle and PS is perpen...

    Text Solution

    |

  7. The radii of the two circles are 19 cm and 9 cm respectively. Find the...

    Text Solution

    |

  8. Two parallel planes which are parallel to the base of a right circular...

    Text Solution

    |

  9. Two make a right circular conical tent 22 metre broad canvas is requir...

    Text Solution

    |

  10. In a right angled triangle the length of the sides containing the righ...

    Text Solution

    |

  11. The lower part of a tent is in the form of a right circular cylinder w...

    Text Solution

    |

  12. In a cuboid, the volume, total surface area and the length of one of i...

    Text Solution

    |

  13. In a Cuboid, the volume, length and the length of its one diagonal are...

    Text Solution

    |

  14. A cylindrical vessel of radius 4 cm contains water. A solid sphere of ...

    Text Solution

    |

  15. By melting a solid iron sphere, 32 conical paper weights of equal volu...

    Text Solution

    |

  16. The ratio of the volumes of a right circular cylinder and a sphere is ...

    Text Solution

    |

  17. If the half total surface area of the cuboid is equal to the square o...

    Text Solution

    |

  18. If 5 cos theta+ 12 sin theta = 13 show that tan theta = 12/5.

    Text Solution

    |

  19. Solve: 4sqrt3 cos^2 theta-4 sin theta +sqrt3 = 0[0^@lethetale90^@]

    Text Solution

    |

  20. Solve: 2 cos theta+ 2sqrt2 = 3 sec theta

    Text Solution

    |