Vectors Question

[Becky2012]

Can someone help me with the attached vectors question?

I've done a:
OF = a + b + c
midpoint of OF = 1/2(a + b+ c)

b: m.p of AG = 1/2(b - a)
m.p of MN = 1/2(c-a)

I don't know how to continue from here.. What does it actually mean when it says that the vectors are concurrent at their point of bisection?

[brightsky]

let X be the midpoint of OF, Y be the midpoint of AG.
as you've already found, OX = 1/2 (a+b+c)
AY = 1/2 (b+c-a)
OY = OA + AY = a + 1/2 (b + c - a) = 1/2 (a+b+c) = OX
so X and Y are the same point.
now
NX = -ON + OX = -(c+1/2 b) + 1/2(a+b+c) = -c - 1/2 b + 1/2 a + 1/2 b + 1/2 c = 1/2 a - 1/2 c = 1/2 (a-c)
NM = -ON + OM = -(c+1/2b) + (a+1/2 b) = -c - 1/2 b + a + 1/2 b = a - c= 1/2 NM
so N, X and M are collinear, with NX = 1/2 NM, and thus NM, OF and AG are concurrent at their point of bisection