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The diagonals of a parallelogram A B C...

The diagonals of a parallelogram `A B C D` intersect at a point `O`. Through `O ,` a line is drawn to intersect `A D\ ` at `P` and `B C` at `Q`. Show that `P Q` divides the parallelogram into two parts of equal area.

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RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions
  1. A B C is a triangle in which D is the mid-point of BC and E is the mid...

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  2. A B C D is a parallelogram X and Y are the mid-points of B C and C D r...

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  3. The diagonals of a parallelogram A B C D intersect at a point O. T...

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  4. The medians B E\ a n d\ C F of a triangle A B C intersect at G. ...

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  5. In Figure, compute the area of quadrilateral A B C D.

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  6. In Figure, P Q R S is a square and T\ a n d\ U are, respectively, ...

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  7. Compute the area of trapezium P Q R S in the given figure.

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  8. In Figure, /A O B=90^@,\ A C=B C ,\ O A=12\ c m\ a n d\ O C=6. 5 c m. ...

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  9. In Figure, A B C D is a trapezium in which A B=7c m ,\ A D=B C=5c m ...

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  10. In Figure, O C D E is a rectangle inscribed in a quadrant of a circl...

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  11. In figure, A B C D is a trapezium in which A B||C D . Prove that: ...

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  12. In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prov...

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  13. Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect eac...

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  14. In Figure, A B C\ a n d\ ABD are two triangles on the base A B. If ...

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  15. If P is any point in the interior of a parallelogram A B C D , then ...

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  16. If A D is a median of a triangle A B C ,\ then prove that triangl...

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  17. A point D is taken on the side B C of a \ A B C such that B D=2D Cd...

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  18. A B C D is a parallelogram whose diagonals intersect at O. If P is a...

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  19. A B C D is a parallelogram in which B C is produced to E such that...

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  20. A B C D is a parallelogram whose diagonals A C\ a n d\ B D intersect...

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