X Y is a line parallel to side B C of /\...

`X Y` is a line parallel to side `B C` of `/_\ A B C`. `B E || AC` and `C F || A B` meet `X Y` in `E` and `F` respectively. Show that `a r( A B E)=a r( A C F)`.

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

X Y is a line parallel to side B C of triangle A B C . If B E II A C and C F II A B meet X Y at E and F respectively.Show that a r( A B E)=a r( A C F)dot

X Y is a line parallel to side B C of triangle A B C. BE ll AC and CF ll AB meet XY in E and F respectively. Show that a r( A B E)=a r( A C F)dot

XY is a line parallel to side BC of a triangle ABC . If B E ||A C and C F\ ||\ A B meet XY at E and F respectively, show that a r\ (A B E)\ =\ a r\ (A C F)

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( /_\A D F)=a r( /_\D C E).

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r(triangle A D F)=a r( triangle D C E) .

O is any point inside a triangle A B C . The bisector of /_A O B ,/_B O C and /_C O A meet the sides A B ,B C and C A in point D ,E and F respectively. Show that A D * B E * C F=D B * E C * F A

In Figure, A B C D ,\ A B F E\ a n d\ C D E F are parallelograms. Prove that a r( /_\A D E)=a r( /_\B C F)

let P an interioer point of a triangle A B C and A P ,B P ,C P meets the sides B C ,C A ,A B in D ,E ,F , respectively, Show that (A P)/(P D)=(A F)/(F B)+(A E)/(E C)dot

In Figure, the incircle of A B C touches the sides B C ,\ C A and A B\ a t\ D ,\ E and F respectively. Show that A F+B D+C E=A E+B F+C D=1/2(P e r i m e t e r\ of\ A B C) .

In Figure, A B C is a right triangle right angled at A ,\ B C E D ,\ A C F G\ a n d\ AB M N are square on the sides B C ,\ C A\ a n d\ A B respectively. Line segment A X\ _|_D E meets B C at Ydot Show that: a r(C Y X E)=a r\ (A C F G)

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

X Y is a line parallel to side B C of triangle A B C . If B E II AC a...
Text Solution
|
E , F , G , H are respectively, the mid-points of the sides A B ,B C ...
Text Solution
|
X Y is a line parallel to side B C of /\ A B C. B E || AC and C F || A...
Text Solution
|
E , F , G , H are respectively, the mid-points of the sides A B ,B C ,...
Text Solution
|
The side A B of a parallelogram A B C D is produced to any point Pdot ...
Text Solution
|
Any point D is taken in the base B C of a triangle A B C\ a n d\ A...
Text Solution
|
In A B C ,D is the mid-point of A B ,P is any point of B CdotC Q P D...
Text Solution
|
In a parallelogram A B C D ,E ,F are any two points on the sides A B a...
Text Solution
|
In Figure, A B C D is a trapezium in which A B||D C .\ \ D C is prod...
Text Solution
|
Prove that the area of an equilateral triangle is equal to (sqrt(3))...
Text Solution
|
In Figure, B C || X Y ,\ B X || C A and A B || Y C. Prove that: a r( A...
Text Solution
|
In Figure, A B C D is a parallelogram. Prove that: a r( B C P)=a r( D ...
Text Solution
|
A B C is a triangle in which D is the mid-point of BC and E is the mid...
Text Solution
|
A B C D is a parallelogram X and Y are the mid-points of B C and C D r...
Text Solution
|
The diagonals of a parallelogram A B C D intersect at a point O. T...
Text Solution
|
The medians B E\ a n d\ C F of a triangle A B C intersect at G. ...
Text Solution
|
In Figure, compute the area of quadrilateral A B C D.
Text Solution
|
In Figure, P Q R S is a square and T\ a n d\ U are, respectively, ...
Text Solution
|
Compute the area of trapezium P Q R S in the given figure.
Text Solution
|
In Figure, /A O B=90^@,\ A C=B C ,\ O A=12\ c m\ a n d\ O C=6. 5 c m. ...
Text Solution
|