USAJMO 2017 Problem 3

Let $ABC$ be an equilateral triangle, and point $P$ on its circumcircle. Let $PA$ and $BC$ intersect at $D$ , $PB$ and $AC$ intersect at $E$ , and $PC$ and $AB$ intersect at $F$ . Prove that the area of $\triangle DEF$ is twice the area of $\triangle ABC$ .

Proposed by Titu Andreescu, Luis Gonzales, Cosmin Pohoata