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SMO 2023 Senior Round 1 Question 21

SMO · SMO 2023 Senior Round 1

Question 21

Let $\triangle ABC$ be an equilateral triangle. $D,E,F$ are points on the sides such that
$$BD:DC=CE:EA=AF:FB=2:1.$$
Suppose the area of the triangle bounded by $AD$, $BE$ and $CF$ is $2023$. Find the area of $\triangle ABC$.

Question illustration