vectors, anyone?

Question

Points P,Q and R are midpoints of sides BC,CA and AB respectively of a triangle ABC. AG=2/3 AP and BG= 2/3 BQ. How to show that CR meets AP and BQ at G if given CG= 2/3 CR, please?
Thank you!

Answer 1

I,m not going to give the entire proof, but I'll point you in the right direction;

Draw QP intersecting CR at X.
Then QP parallel AB and QP = AR = RB.
CX = CR/2
triangle QXC similar triangle ARC
triangle ARG similar triangle PXG
triangle ABG similar triangle PQG

Using the above facts, you can prove CG/CR = 2/3, or
CG = 2/3 CR