In a triangle `A B C ,Da n dE` are points on `B Ca n dA C ,` respectivley, such that `B D=2D Ca n dA E=3E Cdot` Let `P` be the point of intersection of `A Da n dB Edot` Find `B P//P E` using the vector method.

In a triangle A B C , let P a n d Q be points on A Ba n dA C respectively such that P Q || B C . Prove that the median A D bisects P Qdot

In square A B C D ,\ P\ a n d\ Q are mid-point of A B\ a n d\ C D respectively. If A B=8c m\ a n d\ P Q\ a n d\ B D intersect at O , then find area of O P B

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

D a n d E are, respectively, the points on equal sides A B a n d A C of an isosceles triangle A B C such that B , C , E , a n d D are concyclic as shown in Figure. If O is the point of intersection of C D a n d B E , prove that A O is the bisector of line segment D E

In triangle A B C ,poin t sD , Ea n dF are taken on the sides B C ,C Aa n dA B , respectigvely, such that (B D)/(D C)=(C E)/(E A)=(A F)/(F B)=ndot Prove that _(D E F)=(n^2-n+1)/((n+1)^2)_(A B C)dot

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

A B C is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C

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

A B C is a triangle in which D is the mid-point of B C ,\ E\ a n d\ F are mid-points of D C\ a n d\ A E respectively. If area of A B C is 16\ c m^2, find the area of D E F

G is the centroid of triangle A B Ca n dA_1a n dB_1 are rthe midpoints of sides A Ba n dA C , respectively. If "Delta"_1 is the area of quadrilateral G A_1A B_1a n d"Delta" is the area of triangle A B C , then "Delta"//"Delta"_1 is equal to a.3/2 b. 3 c. 1/3 d. none of these