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largest area by 2 cevians in a triangle

Source: 2023 Swedish Mathematical Competition p2

March 24, 2024
geometry

Problem Statement

A triangular colony area is divided into four fields of varying size as shown in the figure below shows. The only other thing we know is that the distances AFAF, FDFD, BFBF and FEFE have the lengths 55, 22, 44 and 22 respectively (in 1010s of m). When the lots are distributed, Joar gets to choose first. Which lot should he choose to get the one with the largest area? https://cdn.artofproblemsolving.com/attachments/9/5/073e2699d54c8ee3a4dd7d23b69c2a894fd93e.png