D and E are points on sides AB and AC respectively of `Delta` ABC such that ar (DBC) = ar EBC). Prove that DE`|\|`BC.

D and E are points on sides AB and AC respectively of tirangle ABC such that ar (DBC) = ar (EBC) . Prove that DE || BC

D and E are points on the sides CA and CB respectively of a triangle ABC right angale at C. prove that AE^(2)+BD^(2)=AB^(2)+DE^(2).

In Delta ABC, D and E are points on side AB and AC respectively such that DE || BC and AD : DB = 3 , If EA = 3.3 cm , them find AC.

In Delta ABC , D and E are points in the sides AB and AC respectively such that DE || BC If AD = 6 cm , DB = 9 cm , and AE = 8 cm find AC.

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=-1

In a Delta ABC , let P and Q be points on AB and AC respectively such that PQ || BC . Prove that the median AD bisects PQ.

In DeltaABC , D and E are points on AB and AC respectively, such that DE||BC . If (AD)/(DB)=4/13 and AC = 20.4 cm, find AE.

If D , E and F are the mid-points of the sides BC , CA and AB respectively of the DeltaABC and O be any point, then prove that OA+OB+OC=OD+OE+OF

In the figure 11.23, E is any point on median AD of a Delta ABC. Show that ar (ABE) = ar (ACE).