The diagonals of a parallelogram A B C...

The diagonals of a parallelogram `A B C D` intersect at `O. A` line through `O` intersects `A B\ ` at `X\ a n d\ D C` at `Y`. Prove that `O X=O Y`.

Text Solution

AI Generated Solution

Topper's Solved these Questions

PROBABILITY
RD SHARMA ENGLISH|Exercise All Questions|67 Videos
RATIONALISATION
RD SHARMA ENGLISH|Exercise All Questions|130 Videos

Similar Questions

Explore conceptually related problems

The diagonals of a parallelogram A B C D intersect at OdotA line through O intersects A B at X and D C at Ydot Prove that O X=O Ydot

The diagonals of a parallelogram A B C D intersect at O . A line through O meets A B\ in X\ a n d\ C D in Y . Show that a r\ (q u a d rilateral A X Y D)=1/2a r(paral l e l ogram\ \ A B C 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) .

The diagonals of a parallelogram A B C D intersect at Odot A line through O meets A B\ in x\ a n d\ C D in Ydot Show that a r\ (A X Y X)=1/2(a r|""|^(gm)\ \ A B C D)

The diagonals of a parallelogram A B C D intersect at Odot A line through O meets A B in X and C D in Ydot Show that a r( A X Y D)=1/2(A R ^(gm)A B C D)

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.

The diagonals of a parallelogram A B C D intersect at a point Odot Through O , a time 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.

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

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 rectangle A B C D intersect in Odot If /_B O C=68^0, find /_O D Adot

RD SHARMA ENGLISH-QUADRILATERALS-All Questions

In Figure, A N and C P are perpendicular to the diagonal B D of a para...
Text Solution
|
In Figure, P Q R S is a parallelogram, P O\ a n d\ Q O are, respective...
Text Solution
|
The diagonals of a parallelogram A B C D intersect at O. A line thro...
Text Solution
|
In Figure, A B C D is a parallelogram and /D A B=60^@. If the bisector...
Text Solution
|
In a parallelogram A B C D , the bisector of /A also bisects B C at X....
Text Solution
|
A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C ...
Text Solution
|
P Q R S is a parallelogram. P X\ a n d\ Q Y are respectively, the p...
Text Solution
|
A B C D is a parallelogram. A B is produced to E so that B E=A B . Pro...
Text Solution
|
Two opposite angles of a parallelogram are (3x-2)^0\ a n d\ \ (50-x)...
Text Solution
|
If an angle of a parallelogram is two-third of its adjacent angle, ...
Text Solution
|
Find the measure of all the angles of a parallelogram, if one angle is...
Text Solution
|
The perimeter of a parallelogram is 22c mdot If the longer side measur...
Text Solution
|
In a parallelogram A B C D ,\ /D=135^0, determine the measures of /...
Text Solution
|
A B C D is a parallelogram in which /A=70^0dot Compute /B ,\ /C\ a n...
Text Solution
|
In Figure, A B C D is a parallelogram in which /A=60^0 . If the bisect...
Text Solution
|
In Figure, A B C D is a parallelogram in which /D A B=75^0a n d\ /D...
Text Solution
|
A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d...
Text Solution
|
Which of the following statements are true (T) and which are false (...
Text Solution
|
Show that if the diagonals of a quadrilateral bisect each other at ...
Text Solution
|
Show that the diagonals of a square are equal and bisect each other...
Text Solution
|