Home
Class 9
MATHS
In the given Fig , Sides AB and AC of a...

In the given Fig
, Sides AB and AC of a `DeltaABC` are produced to E and D respectively. If respective bisectors BO and CO of `angleCBE` and `angleBCD` intersect each other at point O, prove that`angleBOC = 90^@-1/2 angleBAC`.

Promotional Banner

Topper's Solved these Questions

  • Linear Equations In Two Variables

    MBD|Exercise Exercise|92 Videos

  • Number Systems

    MBD|Exercise Exercise|111 Videos

Similar Questions

Explore conceptually related problems

In Fig. 6.38, the sides AB and AC of Delta ABC are produced to points E and D respectively. If bisectors BO and CO of angle CBE and angle BCD respectively meet at point O, then prove that angle BOC = 90^@ -1/2 angle BAC .

In Fig. , sides AB and AC of DeltaABC are extended to points P and Q respectively. Also anglePBC AB .

In Fig. , sides AB and AC of DeltaABC are extended to points P and Q respectively. Also anglePBC AB .

Bisectors of the angles B and C of an isosceles triangle with AB=AC intersect each other at O. BO is produced to a point M. prove that angleMOC=angleABC .

In the fig. triangle AB=AC and bisectors of angleB and angleC meet at a point O. prove that BO=CO and the ray AO is bisector of angleA

In Fig. 6.44, the side QR of triangle PQR is produced to a point S. If the bisectors of angle PQR and angle PRS meet at point T, then prove that angle QTR =1/2 angle QPR .

In fig., two chords AB and CD of a circle intersect each other at point P (when produced) outside the circle prove :- trianglePCA~trianglePDB .

The sides BC, CA and AB of a triangle ABC are of lengths a, b and c respectively. If D is the mid-point of BC and AD is perpendicular to AC, then the value of cos A cos C is:

if a line intersects sides AB and AC of a DeltaABC at D and E respectively and is parallel to BC, prove that (AD)/(AB)=(AE)/(AC) (see Fig. 6,13).

Bisectors of angles B and C of an isoscels triangles ABC with AB=AC intersects each other at O. prove that external angle adjacent to angleABC is equal to angleBOC .

MBD-Lines and Angles-Exercise
  1. Prove that sum of all the interior angles of a pentagon is 540^@.

    Text Solution

    |

  2. Prove that the angle between internal bisector of one base angle and t...

    Text Solution

    |

  3. In the given Fig , Sides AB and AC of a DeltaABC are produced to E an...

    Text Solution

    |

  4. An exterior angle of a triangle is less than either of its interior op...

    Text Solution

    |

  5. Sum of the three angles of a triangle is 180^@.

    Text Solution

    |

  6. Sum of the four angles of a quadrilateral is the four right angles.

    Text Solution

    |

  7. A triangle can have two right angles.

    Text Solution

    |

  8. A triangle can have two acute angles.

    Text Solution

    |

  9. A triangle can have two obtuse angles

    Text Solution

    |

  10. An exterior angle of a triangle is equal to the sum of the two interio...

    Text Solution

    |

  11. Sum of the three angles of a triangle is .............. .

    Text Solution

    |

  12. An exterior angle of a triangle is equal to the two ............. oppo...

    Text Solution

    |

  13. An exterior angle of a triangle is always .................... than ei...

    Text Solution

    |

  14. A triangle cannot have more than ............ right angles

    Text Solution

    |

  15. A triangle cannot have more than ............ obtuse angles.

    Text Solution

    |

  16. Sum of the angles of a quadrilateral is ................ .

    Text Solution

    |

  17. In fig. AB and CD intersect each other at point O. If angleAOC + ang...

    Text Solution

    |

  18. In fig. POQ is a line, anglePOR = 4x and angleQOR = 2x then the valu...

    Text Solution

    |

  19. In the given fig. if angleAOC + angleBOD = 75^@ then the value of an...

    Text Solution

    |

  20. In the fig. value of y is :

    Text Solution

    |