Sorry to bring this up again but could I get help on this problem?
Thanks so much!
Extend the line CG through to meet AB at Z (say).
The medians of a triangle intersect at a point, so CZ will be the third median, so Z will be the midpoint of AB.
Show that ZG is half the length of AB.
(The easiest way to do this is to draw a line from Z, parallel to AY to meet the line BG. Since Z is the midpoint of AB,
this line will bisect BG. Then consider the small right-angled triangle having ZG as its hypotenuse, use Pythagoras.)
Having done that, use the 1/3, 2/3 property for the median CZ.