I am trying to calculate the ratio of CE(green) to BE(blue). Given that FC:FM = 3:1 and it's an equlateral triangle.
I have tried drawing triangles to get an approximation, and I have drawn it in the 3d plane to calculate it but I don't know how to calculate the AE or EF in that matter. How would you go about it? Please just give me a hint not a solution.
Hint: Use the fact that in equilateral triangle we have:
$FH+FG+FM=CM=h$
Show that : $FG=\frac 38 h$
Now use: $FG^2+CG^2=FC^2=(\frac34 h)^2$
which gives CG in terms of h. Similarly find GB in terms of f h. The ratio $\frac{CE}{EB}\approx \frac{CG}{GB}\approx \frac 32$.
Update: Another thing that helps you is using civa's theorem :
$\frac{AM}{MB}\cdot\frac{BE}{EC}\cdot\frac{CH}{HA}=1$