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equal areas (LENDMF)=(ABC)

Source: Mathematics Regional Olympiad of Mexico West 2020 P2

September 9, 2022
geometryequal areas

Problem Statement

Let L L , M M and N N be the midpoints on the sides BC BC , AC AC and AB AB of a triangle ABC ABC . Points D D , E E and F F are taken on the circle circumscribed to the triangle LMN LMN so that the segments LD LD , ME ME and NF NF are diameters of said circumference. Prove that the area of the hexagon LENDMF LENDMF is equal to half the area of the triangle ABC ABC
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