1.Previous
3.Next

F. Then

:

A line through a triangle's median splits the area such that the ratio of the smaller sub-area to the original triangle's area is at least 4/9.

Medians and centroid

The three medians of a triangle each connect a vertex with the midpoint of the opposite side, and the sum of their lengths satisfies

:

Moreover,

:

with equality only in the equilateral case, and for inradius r,

:

If we further denote the lengths

1.Previous
3.Next