Home
Class 10
MATHS
In three line segments OA ,OB and OC , p...

In three line segments `OA ,OB and OC ,` point `L ,M ,N` respectively are so chosen that `LM || AB and MN || BC` but neither of `L ,M ,N` nor of `A , B , C` are collinear. Show that `LN || AC`.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SURFACE AREAS AND VOLUMES

    RD SHARMA ENGLISH|Exercise All Questions|420 Videos

  • TRIGONOMETRIC IDENTITIES

    RD SHARMA ENGLISH|Exercise All Questions|254 Videos

Similar Questions

Explore conceptually related problems

In figure, sides L M and L N of L M N are extended to P and Q respectively. If x > y , show that L M > L N .

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In DeltaABC , if L and M are the points on AB and AC, respectively such that LM || BC . Prove that ar (DeltaLOB) = ar (DeltaMOC) .

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ A B M)=a r\ (\ A C L) .

PQRS is a parallelogram. L and M are points on PQ and SR respectively such that PL = MR. Show that LM and QS bisect each other.

In a \ /_\A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ /_\L C M)=a r\ (/_\ L B M)

If l ,\ m,\n are three lines such that l || m\ a n d\ n_|_l , prove that n_|_mdot

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ L O B)=a r\ (\ M O C) .

L and M are the mid-points of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.

In a triangle \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (triangle \ L O B)=a r\ (triangle \ M O C)

RD SHARMA ENGLISH-TRIANGLES-All Questions
  1. In Figure, A B C is a triangle in which A B=A Cdot Point D and E are p...

    Text Solution

    |

  2. The bisector of interior angleA of triangleABC meets BC and D and the ...

    Text Solution

    |

  3. In three line segments OA ,OB and OC , point L ,M ,N respectively are ...

    Text Solution

    |

  4. O is any point inside a triangle A B C . The bisector of /A O B ,/B O ...

    Text Solution

    |

  5. ABCD is a quadrilateral in which AB=AD . The bisector of  BAC a...

    Text Solution

    |

  6. In /\A B C ,D is the mid-point of BC and ED is the bisector of the /A...

    Text Solution

    |

  7. A D is a median of Delta A B C . The bisector of /A D B and /A D C...

    Text Solution

    |

  8. In Figure, A B C is a right triangle right angled at B and points Da n...

    Text Solution

    |

  9. In a triangle A B C , the angles at B and C are acute. If BE and CF b...

    Text Solution

    |

  10. Prove that in any triangle the sum of squares of any two sides is equa...

    Text Solution

    |

  11. AD is an altitude of an equilateral triangle ABC. On AD as base...

    Text Solution

    |

  12. A ladder 15 m long reaches a window which is 9 m above the ground o...

    Text Solution

    |

  13. Prove that three times the sum of the squares of the sides of a tri...

    Text Solution

    |

  14. In Figure, D , E are points on sides A B and A C respectively of /\A ...

    Text Solution

    |

  15. In the trapezium ABCD,AC and BD intersect at O and also AB=2CD If the ...

    Text Solution

    |

  16. ABC is an isosceles triangle right-angled at B. Similar triangles ...

    Text Solution

    |

  17. In Figure, DE||BC and AD : D B=4: 5. Find (A r e a( D E F))/(A r e a( ...

    Text Solution

    |

  18. ABC is a right triangle right-angled at B. Let D and E be any points o...

    Text Solution

    |

  19. P and Q are the mid-points of the CA and CD respectively of a tri...

    Text Solution

    |

  20. A girl of height 90 cm is walking away from the base of a lamp-post...

    Text Solution

    |