Finding Ratios Using Mass Points in Triangles with Four Points

[soopo]

Homework Statement

Find the ratio EHG. Please, see the full question with a picture here: https://dl.getdropbox.com/u/175588/problem.JPG

Homework Equations

"In triangle ABC, let D and E be the trisection points of BC with D between B and E." Please, see the full question with a picture here: https://dl.getdropbox.com/u/175588/problem.JPG

The Attempt at a Solution

I am unable to calculate mass points to a line with four mass points.

 

[Billy Bob]

First draw in CG and deal with triangle ABC with segments CG and DF which intersect at a point, call it X. Find the location of X.

Then deal with triangle CGD.

This way you avoid dealing with "four all at once."

 

[soopo]

First draw in CG and deal with triangle ABC with segments CG and DF which intersect at a point, call it X. Find the location of X.

Then deal with triangle CGD.

This way you avoid dealing with "four all at once."

So if we can serve one point in only one way, we are done. The point could also be served by other triangles but we must stick to the one we choose, just like you choose consider CDG.

Thank you for your answer!