A point `D` is taken on the side `B C` of a `\ A B C` such that `B D=2D Cdot` Prove that `a r\ (\ A B D)=\ 2\ a r\ (\ A D C)`

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

A point D is taken on the side B C of a A B C such that B D=2d Cdot Prove that a r( A B D)=2a r( A D C)dot

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F Cdot Prove that: a r\ (\ E B G)=a r\ (\ E F C)

A point D is on the side B C of an equilateral triangle A B C such that D C=1/4\ B C . Prove that A D^2=13\ C D^2 .

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

In Figure D\ a n d\ E are two points on B C such that B D=D E=E Cdot Show that a r(\ A B D)=\ a r\ (\ A D E)=a r\ (\ A E C)dot

D is a point on the side B C of A B C such that /_A D C=/_B A C . Prove that (C A)/(C D)=(C B)/(C A) or, C A^2=C BxxC D .

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

A B C D is a parallelogram, G is the point on A B such that A G=2G B ,E is a point of D C such that C E=2D E and F is the point of B C such that B F=2F Cdot Prove that : a r(A D E G)=a r(G B C E) a r( E G B)=1/6a r(A B C D)