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IMO 1966 - Official Contest Problems Question 6

IMO · IMO 1966 - Official Contest Problems

Question 6

(POL) Let $M,K,L$ be points on $(AB),(BC),(CA)$, respectively. Prove that the area of at least one of the three triangles $\triangle MAL$, $\triangle KBM$, and $\triangle LCK$ is less than or equal to one-fourth the area of $\triangle ABC$.