lengths of the cevians passing through P are inversely proportional sidelengths
Source: 2012 Sharygin Geometry Olympiad Final Round 10.2
August 3, 2018
geometryratiosCevian
Problem Statement
We say that a point inside a triangle is good if the lengths of the cevians passing through this point are inversely proportional to the respective side lengths. Find all the triangles for which the number of good points is maximal.(A.Zaslavsky, B.Frenkin)