Diagonals A C\ a n d\ B D of a quadril...

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)`

Topper's Solved these Questions

ALGEBRAIC IDENTITIES
RD SHARMA ENGLISH|Exercise All Questions|247 Videos
CIRCLE
RD SHARMA ENGLISH|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

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

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\ a n d\ B D of a trapezium A B C D with A B||D C intersect each other at O . Prove that a r\ ( A O D)=\ a r\ ( B O C) .

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.

In Figure, diagonals AC and BD of quadrilateral ABCD intersect at O such that O B = O D . If A B = C D , then show that: (i) a r /_\(D O C) = a r /_\(A O B) (ii) a r /_\(D C B) = a r /_\(A C B) (iii) D A || CB

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)

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.

In Figure, A B C D\ a n d\ A E F D are two parallelograms? Prove that: a r\ (\ A P E):\ a r\ (\ P F A)=\ a r\ \ (Q F D)\ : a r\ (\ P F D)

A B C D is a parallelogram whose diagonals A C\ a n d\ B D intersect at O . A line through O intersects A B\ a t\ P\ a n d\ D C\ at Q . Prove that a r\ (\ /_\P O A)=\ a r\ (\ /_\Q O C) .

In Figure, P is a point in the interior of a parallelogram A B C Ddot Show that a r( A P B)+a r( P C D)=1/2a r\ (|""|^(gm)A B C D) a r\ ( A P D)+a r\ ( P B C)=a r\ ( A P B)+a r( P C D)

RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions

In figure, A B C D is a trapezium in which A B||C D . Prove that: ...
Text Solution
|
In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prov...
Text Solution
|
Diagonals A C\ a n d\ B D of a quadrilateral A B C D intersect eac...
Text Solution
|
In Figure, A B C\ a n d\ ABD are two triangles on the base A B. If ...
Text Solution
|
If P is any point in the interior of a parallelogram A B C D , then ...
Text Solution
|
If A D is a median of a triangle A B C ,\ then prove that triangl...
Text Solution
|
A point D is taken on the side B C of a \ A B C such that B D=2D Cd...
Text Solution
|
A B C D is a parallelogram whose diagonals intersect at O. If P is a...
Text Solution
|
A B C D is a parallelogram in which B C is produced to E such that...
Text Solution
|
A B C D is a parallelogram whose diagonals A C\ a n d\ B D intersect...
Text Solution
|
A B C D is a parallelogram. E is a point on B A such that B E=2\ E A...
Text Solution
|
In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points o...
Text Solution
|
In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points o...
Text Solution
|
In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points o...
Text Solution
|
A B C D is a parallelogram, G is the point on A B such that A G=...
Text Solution
|
A B C D is a parallelogram, G is the point on A B such that A G=2\...
Text Solution
|
A B C D is a parallelogram, G is the point on A B such that A G=2\...
Text Solution
|
In figure, ABCD is a parallelogram, AE perpendicular to DC and CF perp...
Text Solution
|
In Figure, C D\ || A E\ a n d\ C Y || B A. (i) Name a triangle equa...
Text Solution
|
In figure, P S D A is a parallelogram in which P Q=Q R=R S\ a n d\ A...
Text Solution
|