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Found problems: 51

1964 Czech and Slovak Olympiad III A, 4
Tags: geometry , geometric construction , equilateral , triangle
Points $A, S$ are given in plane such that $AS = a > 0$ as well as positive numbers $b, c$ satisfying $b < a < c$. Construct an equilateral triangle $ABC$ with the property $BS = b$, $CS = c$. Discuss conditions of solvability.