`A B C D` is a trapezium such that `B C || A D` and `A B=4c m` . If the diagonals `A C` and `B D` intersect at `O` such that `(A O)/(O C)=(D O)/(O B)=1/2` , then `B C=` `7c m` (b) `8c m` (c) `9c m` (d) `6c m`

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))

Medians of A B C intersect at G . If a r\ ( A B C)=27\ c m^2, then a r\ ( A B G C)= 6\ c m^2 (b) 9\ c m^2 (c) 12\ c m^2 (d) 18 c m^2

Line segments A B a n d C D intersect at O such that A C D Bdot If /_C A B=45^0a n d /_C D B=55^0, then /_B O D= 100^0 (b) 80^0 (c) 90^0 (d) 135^0

In a A B C if D\ a n d\ E are mid-points of B C\ a n d\ A D respectively such that a r\ ( A E C)=4\ c m^2 , then a r\ ( B E C)= 4\ c m^2 (b) 6\ c m^2 (c) 8\ c m^2 (d) 12 c m^2

A B C D is a trapezium in which A B D Cdot If a r( A B D)=24\ c m^2a n d\ A B=8\ c m , then height of A B C is 3 cm (b) 4 cm (c) 6 cm (d) 8 cm

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

The diagonals of a parallelogram A B C D intersect at O . If /_B O C=90^0\ a n d\ /_B D C=50^0, then /_O A B= 40^0 (b) 50^0 (c) 10^0 (d) 90^0

Diagonals A C a n d B D of a quadrilateral A B C D intersect at O in such a way that a r ( A O D)=a r ( B O C)dot Prove that A B C D is a trapezium.

Diagonals A C and B D of a quadrilateral A B C D intersect at O in such a way that a r( A O D)=a r( B O C) . Prove that A B C D is a trapezium.

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.