Home
Class 9
MATHS
In A B C ,A B=A C , and the bisectors...

In `A B C ,A B=A C ,` and the bisectors of angles `B` and `C` intersect at point `O` . Prove that `B O=C O` and the ray `A O` is the bisector of angles `B A Cdot`

Text Solution

Verified by Experts

To prove- BO=CO and `/_BAO=/_CAO`
Proof- `In/_ABC`
`AB=AC`
`/_B=/_C`
`1/2/_B=1/2/_C`
`/_QBC=/_QCB`
`In/_OBC`
`/_OBC=/_QCB`
...
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    RD SHARMA ENGLISH|Exercise All Questions|306 Videos
  • CONSTRUCTION

    RD SHARMA ENGLISH|Exercise All Questions|40 Videos

Similar Questions

Explore conceptually related problems

In A B C ,\ A B=A C , and the bisectors of angles B\ a n d\ C intersect at point Odot Prove that B O=C O\ and the ray A O is the bisector of angle B A C

In DeltaABC,AB=AC and the bisectors of angles B and C intersect at point O. Prove that BO=OC

In Delta ABC , AB = AC and the bisectors of angles B and C intersect at point O. Prove that : (i) BO = CO (ii) AO bisects angle BAC.

In A B C , if /_B=60^0,\ /_C=80^0 and the bisectors of angles /_A B C\ a n d\ /_A C B meet at a point O , then find the measure of /_B O C.

In A B C ,/_B=2/_C and the bisector of /_B intersects A C at Ddot Prove that (B D)/(D A)=(B C)/(B A)

In a A B C , it is given that A B=A C and the bisectors of /_B and /_C intersect at O , If M is a point on B O produced, prove that /_M O C=/_A B Cdot

In triangle ABC,the bisector of interior angle A and the bisector angle C meet at point O. Prove that angle AOC=(1)/(2)angleB

In a A B C , it is given that A B=A C and the bisectors of /_B\ a n d\ C intersect at Odot If M is a point on B O produced, prove that /_M O C=\ /_A B C

In a triangle A B C ,/_A B C=/_A C B and the bisectors of /_A B C and /_A C B intersect at O such that /_B O C=120^0dot Show that /_A=/_B=/_C=60^0

B D and C E are bisectors of /_B and /_C of an isosceles A B C with A B=A Cdot Prove that B D=C Edot

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. If the altitudes from two vertices of a triangle to the opposite si...

    Text Solution

    |

  2. A D and B C are equal perpendiculars to a line segment A B . Show that...

    Text Solution

    |

  3. In A B C ,A B=A C , and the bisectors of angles B and C intersec...

    Text Solution

    |

  4. In Figure, it is given that A B=E F ,B C=D E ,A B|B D and F E|C Edot P...

    Text Solution

    |

  5. In Figure, it is given that A B=B C and A D=E C . Prove that A B E~=C ...

    Text Solution

    |

  6. In Figure, l II m and M is the mid-point of the line segment A Bdot P...

    Text Solution

    |

  7. In Figure, line l is the bisector of angle A and B is any point on l ....

    Text Solution

    |

  8. In Figure, O is the mid point of A B and C D . Prove that (i) A O C~...

    Text Solution

    |

  9. Prove that measure of each angle of an equilateral triangle is 60^0...

    Text Solution

    |

  10. In Figure, it is given that A E=A D and B D=C Edot Prove that triangl...

    Text Solution

    |

  11. In Figure, it is given that A B=C F ,E F=B D and /A F E=/C B Ddot Prov...

    Text Solution

    |

  12. Two triangles are congruent if two sides and the included angle of ...

    Text Solution

    |

  13. In DeltaABC ,/A=100^0 and A B=A Cdot Find /B and /C

    Text Solution

    |

  14. Angles opposite to two equal sides of a triangle are equal. GIVEN :...

    Text Solution

    |

  15. In Figure, X and Y are two points on equal sides A B and A C of a A B ...

    Text Solution

    |

  16. Prove that the angle between internal bisector of one base angle an...

    Text Solution

    |

  17. In A B C and P Q R Figure, A B=P Q ,B C=Q R and C B and R Q are extend...

    Text Solution

    |

  18. In Figure, the side B C of A B C is produced to form ray B D as shown....

    Text Solution

    |

  19. In a triangle the greater angle has the longer side opposite to it.

    Text Solution

    |

  20. If the bisectors of the base angles of a triangle enclose an angle ...

    Text Solution

    |