Home
Class 9
MATHS
In a parallelogram A B C D diagonals A C...

In a parallelogram `A B C D` diagonals `A C` and `B D` intersect at `O` and `A C=6. 8c m` and `B D=13. 6c mdot` Find the measures of `O C` and `O Ddot`

Text Solution

AI Generated Solution

To find the measures of \( OC \) and \( OD \) in the parallelogram \( ABCD \), where the diagonals \( AC \) and \( BD \) intersect at point \( O \), we can follow these steps: ### Step-by-Step Solution: 1. **Understand the Properties of Parallelograms**: In a parallelogram, the diagonals bisect each other. This means that the point where they intersect divides each diagonal into two equal parts. 2. **Identify the Lengths of the Diagonals**: ...
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    RD SHARMA|Exercise All Questions|67 Videos

  • RATIONALISATION

    RD SHARMA|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

In a parallelogram A B C D diagonals A C\ a n d\ B D intersect at O\ a n d\ A C=6. 8\ c m\ a n d\ B D=5. 6 c m . Find the measures of O C\ a n d\ O D .

A B C D is a parallelogram whose diagonals A C and B D intersect at Odot A Line through O intersects A B at P and D C at Qdot Prove that a r( P O A)=a r( Q O C)dot

Show that the diagonals of a parallelogram divide it into four triangles of equal area. GIVEN : A parallelogram A B C D . The diagonals A C and B D intersect at Odot TO PROVE : a r( O A B)=a r( O B C)=a r( O C D)=a r( A O D)

In Figure, /_A O B=90^0,\ A C=B C ,\ O A=12\ c m\ a n d\ O C=6. 5 c mdot Find the area of A O Bdot

In a quadrilateral A B C D , bisectors of angles A\ a n d\ B intersect at O such that /_A O B=75^0, then write the value of /_C+\ /_D

If the diagonals A C ,B D of a quadrilateral A B C D , intersect at O , and seqarate the quadrilateral into four triangles of equal area, show that quadrilateral A B C D is a parallelogram. GIVEN : A quadrilateral A B C D such that its diagonals A C and B D intersect at O and separate it into four parts such that a r( A O B)=a r( B O C)=a r( C O D)=a r( A O D) TO PROVE : Quadrilateral A B C D is a parallelogram.

A B C D is a trapezium in which A B C D . The diagonals A C and B D intersect at O . Prove that (i) A O B C O D (ii) If O A=6c m , O C=8c m , Find: (A r e a ( A O B))/(A r e a ( C O D)) (b) (A r e a ( A O D))/(A r e a ( C O D))

In a parallelogram A B C D , A B=10 c m , A D=6c mdot The bisector of /_A meets D C in E , A E a n d B C produced meet at Fdot Find the length C Fdot

In Figure, A B C D is a quadrilateral in which diagonal \ A C=84\ c m ; D L_|_A C ,\ B M_|_A C ,\ D L=16. 5\ c m and B M=12\ c m . Find the area of quadrilateral A B C Ddot

In Figure, A B C D is a parallelogram, A E _|_D C a n d CC F_|_A D . If A B=16 C M , A E=8c m a n d C F=10 c m , find A D

RD SHARMA-QUADRILATERALS-All Questions
  1. In a parallelogram A B C D , prove that sum of any two consecutive ang...

    Text Solution

    |

  2. A B C D is a parallelogram andline segments A X ,C Y bisect the angles...

    Text Solution

    |

  3. In a parallelogram A B C D diagonals A C and B D intersect at O and A ...

    Text Solution

    |

  4. In a parallelogram, the bisectors of any two consecutive angles inte...

    Text Solution

    |

  5. The diagonals of a parallelogram bisect each other.

    Text Solution

    |

  6. The angle bisectors of a parallelogram form a rectangle.

    Text Solution

    |

  7. If diagonal of a parallelogram bisects one of the angles of the par...

    Text Solution

    |

  8. Show that the quadrilateral, formed by joining the mid-points of the ...

    Text Solution

    |

  9. The diagonals of a quadrilateral A B C D are perpendicular. Show that ...

    Text Solution

    |

  10. ABCD is a rhombus and P ,Q ,R ,S are the mid-points of A B ,B C ,C D ,...

    Text Solution

    |

  11. Show that the quadrilateral formed by joining the mid-points of the ...

    Text Solution

    |

  12. Prove that the figure formed by joining the mid-points of the pair of ...

    Text Solution

    |

  13. In Figure, A D is the median and D E A Bdot Prove that B E is the med...

    Text Solution

    |

  14. In a A B C , find the measures of the angles of the triangle formed b...

    Text Solution

    |

  15. In A B C ,A D is the median through A and E is the mid-point of A D ....

    Text Solution

    |

  16. In Figure, A D , and B E are medians of A B C and B E || D Fdot Prove...

    Text Solution

    |

  17. P ,Q and R are, respectively, the mid-points of sides B C ,C A and A B...

    Text Solution

    |

  18. P is the mid-point of side A B of a parallelogram A B C D . A Line thr...

    Text Solution

    |

  19. In Figure, A B C D isa trapezium in which side A B is a parallel to si...

    Text Solution

    |

  20. In Figure, A B C D is a parallelogram. E and F are the mid-points of t...

    Text Solution

    |