MathNet 2020 — Math Olympiad Vault — Part 06 Question 21

Let $O$ be an interior point of triangle $ABC$, and let $M,N,P$ be the intersections of $AO$ with $BC$, $BO$ with $CA$, and $CO$ with $AB$, respectively. Prove that at least two of the six resulting triangles have area at most $[ABC]/6$.