In `DeltaABC`, 'O' is the orthocentre, M is midpoint of BC and `angleBAC = 30^(@)`. The segment OM is produced to the point T such that OM = MT. Prove that AT=2BC.

In DeltaABC , centroid = (2, 0). If (1, 3) is the midpoint of BC, then A =

In DeltaABC if r_(1)=2r_(1)=3r_(3) and D is the mid point of BC then cos angle ADC=

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB .

In DeltaABC , if D is the midpoint of BC then prove that bar(AD)=(bar(AB)+bar(AC))/2

In DeltaOAB , L is the midpoint of OA and M is a point on OB such that (OM)/(MB)=2 . P is the mid point of LM and the line AP is produced to meet OB at Q. If bar(OA)=bar(a), bar(OB)=bar(b) then find vectors bar(OP) and bar(AP) interms of bar(a) and bar(b) .

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF=2AB .

In DeltaABC ,BC=8cm and D, E are the midpoints of AB and AC, also AF=1/2 AD and AG=1/2 AE , then FG=

In an equilateral Triangle ABC,D is a point on side BC such that BD=1/3BC . Prove that 9AD^2=7AB^2 .

In DeltaABC, B=(0,0), AB=2, angleABC=pi/3 and the middle point of BC has the co-ordinates (2,0). Then the centroid of triangle is

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.