Home
Class 9
MATHS
O is any point in the exterior of a Delt...

O is any point in the exterior of a `DeltaABC`. Prove that `2(OA + OB + OC) > (AB + BC + CA)`
.

Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    MODERN PUBLICATION|Exercise EXERCISE|98 Videos

  • SURFACE AREAS AND VOLUMES

    MODERN PUBLICATION|Exercise EXERCISE|228 Videos

Similar Questions

Explore conceptually related problems

O is any point in the interior of triangleABC such that OB=OC and AB=AC. Show that AO bisects angleA .

D is any point on the base BC, produced of an isosceles triangle ABC, prove that AD>AB.

O is any point inside a rectangle ABCD (see Fig. 6.52). Prove that OB^2 + OD^2 = OA^2 + OC^2 .

In fig., O is a point in the interior of a triangle ABC, OD bot BC, OE bot AC and OF bot AB. Show that:- OA^2+OB^2+OC^2-OD^2-OE^2-OF^2=AF^2+BD^2+CE^2 .

If O is the circumcentre, G is the centroid and O' the orthocenter of DeltaABC prove that (i) SA+SB+SC=3SG, where S is any point in the plane of DeltaABC . (ii) OA+OB+OC=OO' Where, AP is diameter of the circumcircle.

If G be the centroid of a triangle ABC, prove that, AB^2+BC^2+CA^2=3(GA^2+GB^2+GC^2)

If O and H be the circumcentre and orthocentre respectively of triangle ABC, prove that vec OA+ vec OB+ vec OC= vec OH .

AD is a median of DeltaABC . Is AB + BC + CA gt 2AD ?

Draw any circle and mark: a point in its exterior

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

MODERN PUBLICATION-TRIANGLES-EXERCISE
  1. In the trianglePQR, S is any point on the side QR show that PQ+QR+RP+2...

    Text Solution

    |

  2. O is any point in the exterior of a DeltaABC. Prove that 2(OA + OB + O...

    Text Solution

    |

  3. O is any point in the exterior of a DeltaABC. Prove that 2(OA + OB + O...

    Text Solution

    |

  4. O is any point in the exterior of a DeltaABC. Prove that 2(OA + OB + O...

    Text Solution

    |

  5. In the fig. O is the centre of the circle and XOY is diameter. If XZ i...

    Text Solution

    |

  6. The measure of each angle of an equilateral triangle is :

    Text Solution

    |

  7. In two triangles, ABC and ADC, if AB=AD, BC=CD. Are they congruent?

    Text Solution

    |

  8. If two congruent triangles ABC and DEF, if AB=DE and BC=EF. Name the p...

    Text Solution

    |

  9. In two triangles ABC and DEF, angleA=angleD,angleB=angleE and angleC=a...

    Text Solution

    |

  10. ABC is an isosceles triangle AB=AC and BD and CE are its two medians. ...

    Text Solution

    |

  11. CDE is an equilateral triangle formed on a side CD of a square ABCD(se...

    Text Solution

    |

  12. In the fig. prove that: AD+AB+BC+CD>2AC.

    Text Solution

    |

  13. In the fig. find x and y

    Text Solution

    |

  14. ABC is an isosceles triangle with AB = AC and AD is one of its altitud...

    Text Solution

    |

  15. In triangleABC, AB=AC and angleA=100^@, find angleB and angleC.

    Text Solution

    |

  16. Sum of any two sides of a triangle is greater than the third side.

    Text Solution

    |

  17. In a triangle, the angle opposite to the longer side is :

    Text Solution

    |

  18. The sides opposite to two equal angles of a triangle are :

    Text Solution

    |

  19. If altitudes from two vertices of a triangle to the opposite sides are...

    Text Solution

    |

  20. State True or false Bisectors of unequal angle of an triangle may be ...

    Text Solution

    |