Thanks for the help
Hello,Originally Posted by eekoz
1. I've attached a diagram to demonstrate what I've calculated.
2. You ought to know that the vector $\displaystyle (OM_{BC})=\frac{1}{2}((OB)+(OC))$
3. You get three equations, which always describe the vector (OG):
$\displaystyle (OG)=(OA)+k \cdot \left(\frac{1}{2} \cdot ((OB)+(OC))-(OA) \right)$
$\displaystyle (OG)=(OB)+t \cdot \left(\frac{1}{2} \cdot ((OA)+(OC))-(OB) \right)$
$\displaystyle (OG)=(OC)+s \cdot \left(\frac{1}{2} \cdot ((OB)+(OA))-(OC) \right)$
Expand the RHS of this equations. You'll get a system of three linear equations. Solve for k, t, s. You'll get k = t = s = 2/3.
If you plug in this value into one of the equations above and you'll get your proof.
Hope that this is of some help.
Greetings
EB