IMO Shortlist 1969 problem 57
Dodao/la:
arhiva2. travnja 2012. Given triangle

with points

and

are in the sides

and

respectively.
If

, then prove that the centroid of

lies on

.
%V0
Given triangle $ABC$ with points $M$ and $N$ are in the sides $AB$ and $AC$ respectively.
If $\dfrac{BM}{MA} +\dfrac{CN}{NA} = 1$ , then prove that the centroid of $ABC$ lies on $MN$ .
Izvor: Međunarodna matematička olimpijada, shortlist 1969