If B is the mid point of `bar (AC)` and C is the mid point of `bar(BD)` where A,B,C,D lie on a straight line ,say why `AB=CD`?

Verify whether D is the mid point of bar (AG) .

If O is origin and C is the mid - point of A (2, -1) and B ( -4, 3) . Then value of OC is

In the figure, M is the mid-point of [AB] and N is the mid-point of [CD] and O is the mid-point of [MN]. Prove that : vec(BC)+vec(AD)=2vec(MN) .

In triangleABC , D is the mid point of the side AB and E is centroid of triangleCDA . If OE*CD=0 , where O is the circumcentre of triangleABC , using vectors prove that AB=AC.

In a triangle ABC, D is the mid point of side AC such that BD=1/2AC . Show that angleABC is a right angle.

If ABC is triangle and D is the mid-point of [BC], prove that vec AB + vec AC= 2 vec AD .

In the fig. l||m and O is the mid point of the line segment. Prove that O is also the mid point of any line segment CD having its end points on l and m respectively

In the figure X and Y are the mid-points of AC and AB respectivley, QP||BC and CYQ and BXP are striaght lines. Prove that ar(ABP) = ar(ACQ)