The diagonals of quadrilateral `A B C D` intersect at `O` . Prove that `(a r( A C B))/(a r( A C D))=(B O)/(D O)`

The diagonals of a quadrilateral ABCD intersect each other at the point O such that (A O)/(B O)=(C O)/(D O) . Show that ABCD is a trapezium.

In figure ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (a r(A B C))/(a r(D B C))=(A O)/(D O) .

The diagonals of quadrilateral A B C D ,A C and B D intersect in Odot Prove that if B O=O D , the triangles A B C and A D C are equal in area. GIVEN : A quadrilateral A B C D in which its diagonals A C and B D intersect at O such that B O = O Ddot TO PROVE : a r( A B C)=a r( A D C)

The diagonals of quadrilateral A B C D ,\ A C\ a n d\ B D intersect in O . Prove that if B O=O D , the triangles A B C\ a n d\ A D C are equal in area.

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

Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect each at P . Show that: a r(/_\A P B)\ x \ a r\ (/_\ C P D) = \ a r\ (\ /_\A P D)\ \ x a r\ (\ /_\P B C)

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A and C . Prove that A B=A D and C B=CD .

In the figure, diagonal A C of a quadrilateral A B C D bisects the angles A and C . Prove that A B=A D and C B=CD

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that a r\ (A P B)\ xx\ a r\ (C P D)\ =\ a r\ (A P D)\ xx\ a r\ (B P C)dot