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Equilateral triangle

Source: Czech and Slovak Olympiad 1964, National Round, Problem 4

June 23, 2024
geometrygeometric constructionEquilateralTriangle

Problem Statement

Points A,SA, S are given in plane such that AS=a>0AS = a > 0 as well as positive numbers b,cb, c satisfying b<a<cb < a < c. Construct an equilateral triangle ABCABC with the property BS=bBS = b, CS=cCS = c. Discuss conditions of solvability.
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