MathDB
equal distances , point in equilateral (2016 Novosibirsk Oral Geo Oly 8-9 p6)

Source:

April 26, 2021
geometryequal segmentsEquilateral

Problem Statement

An arbitrary point MM inside an equilateral triangle ABCABC was connected to vertices. Prove that on each side the triangle can be selected one point at a time so that the distances between them would be equal to AM,BM,CMAM, BM, CM.