Home
Class 9
MATHS
O is any point in the interior of A ...

`O` is any point in the interior of ` A B Cdot` Prove that `A B+A C > O B+O C` `A B+B C+C A > O A+O B+O C` `O A+O B+O C >1/2(A B+B C+C A)`

Text Solution

AI Generated Solution

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

O is a point in the exterior of A B Cdot what symbol > , 1/2(A B+B C+C A)

A B C D is a parallelogram and O is any point in its interior. Prove that: (i) a r\ ( A O B)+a r\ (C O D)=1/2\ a r(A B C D) (ii) a r\ ( A O B)+\ a r\ ( C O D)=\ a r\ ( B O C)+\ a r( A O D)

O is any point inside a rectangle ABCD. Prove that O B^2+O D^2=O A^2+O C^2 .

O is any point inside a rectangle ABCD. Prove that O B^2+O D^2=O A^2+O C^2 .

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( /_\O A B)=a r( /_\O B C)

In Figure O is the mid-point of A B\ a n d\ C Ddot Prove that \ A O C~=\ \ B O D (b) A C=B D (iii) A C||B D

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

In figure, O is a point in the interior of a triangle ABC, O D_|_B C ,O E_|_A C and O F_|_A B . Show that (i) O A^2+O B^2+O C^2-O D^2-O E^2-O F^2=A F^2+B D^2+C E^2 (ii) A F^2+B D^2+C E^2=A E^2+C D^2+B F^2

O is any point on the diagonal B D of the parallelogram A B C D . Prove that a r( triangle O A B)=a r(triangle O B C)

In A B C ,\ \ /_A=60o . Prove that B C^2=A B^2+A C^2-A B.A C .

RD SHARMA ENGLISH-CONGRUENT TRIANGLE -All Questions
  1. Is it possible to draw a triangle with sides of length 2c m ,\ 3c m...

    Text Solution

    |

  2. In A B C ,\ /B=35^0,/C=65^0 and the bisector of /B A C meets B C in P...

    Text Solution

    |

  3. O is any point in the interior of A B Cdot Prove that A B+A C > O...

    Text Solution

    |

  4. Prove that the perimeter of a triangle is greater than the sum of i...

    Text Solution

    |

  5. Prove that in a quadrilateral the sum of all the sides is greater t...

    Text Solution

    |

  6. In Figure, prove that C D+D A+A B+B C >2A C

    Text Solution

    |

  7. Which of the following statements are true (T) and which are false (...

    Text Solution

    |

  8. Fill in the blanks to make the following statements true: In a righ...

    Text Solution

    |

  9. In two congruent triangles A B C\ a n d\ D E F , if A B=D E\ a n d\...

    Text Solution

    |

  10. In two triangles A B C\ a n d\ D E F , it is given that /A=/D ,\ /B=/E...

    Text Solution

    |

  11. If A B C\ a n d\ D E F are two triangles such that A C=2. 5\ c m ,\ ...

    Text Solution

    |

  12. In two triangles A B C\ a n d\ A D C , if A B=A D\ a n d\ B C=C Ddot A...

    Text Solution

    |

  13. In triangle A B C\ a n d\ C D E , if A C=C E ,\ B C=C D ,\ /A=60^0,\ /...

    Text Solution

    |

  14. A B C is an isosceles triangle in which A B=A C,B E\ a n d\ C F are ...

    Text Solution

    |

  15. Find the measure of each angle of an equilateral triangle.

    Text Solution

    |

  16. Delta C D E is an equilateral triangle formed on a side C D of a squ...

    Text Solution

    |

  17. Show that the sum of the three altitudes of a triangle is less than...

    Text Solution

    |

  18. In Figure, if A B=A C\ a n d\ /B=/Cdot Prove that B Q=C P

    Text Solution

    |

  19. If A N C~= L K M , then side of L K M equal to side A C\ of A B C ...

    Text Solution

    |

  20. If A B C\ ~= A C B , then A B C is isosceles with (a)A B=A C (b) ...

    Text Solution

    |