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min perimeter of ABC, if 6 cevians divide the sides into 6 integer lengths

Source: 2019 Dürer Math Competition Finals Day2 E+3 https://artofproblemsolving.com/community/c1621835_2019_

January 5, 2022
geometryperimeterGeometric Inequalities

Problem Statement

Let PP be an interior point of triangle ABCABC. The lines APAP, BPBP and CPCP divide each of the three sides into two segments. If the so-obtained six segments all have distinct integer lengths, what is the minimum possible perimeter of ABCABC?
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