In a `triangle OAB`,E is the mid point of OB and D is the point on AB such that `AD:DB=2:1` If OD and AE intersect at P then determine the ratio of `OP: PD` using vector methods

In a triangle ABC,D is the mid - point of BC, AD is produced upto E so that DE = AD. Prove that : AB=EC

In a triangle ABC , E is the mid-point of median AD . Show that a r\ (B E D)=1/4a r\ (A B C)

In triangle ABC, AB > AC. E is the mid-point of BC and AD is perpendicular to BC. Prove that : AB^2 +AC^2=2AE^2 +2BE^2

In an equilateral triangle ABC , D is the mid-point of AB and E is the mid-point of AC. Find the ratio between ar ( triangleABC ) : ar(triangleADE)

In the triangle OAB , M is the midpoint of AB, C is a point on OM, such that 2 OC = CM . X is a point on the side OB such that OX = 2XB. The line XC is produced to meet OA in Y. Then (OY)/(YA)=

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A D . Prove that area of B E D = 1/4 area of ABC.

In triangle ABC, P is mid-point of AB and Q is mid-point of AC. If AB = 9.6 cm, BC = 11 cm and AC = 11.2 , find the perimeter of the trapezium PBCQ.

In triangle ABC, D is a point in side AB such that AB = 4AD and E is a point in AC such that AC = 4AE. Show that BC : DE = 4:1

In triangle ABC, M is mid-point of AB, N is mid-point of AC and D is any point in base BC. Use Intercept Theorem to show that MN bisects AD.