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If possible, construct an equilateral triangle whose three vertices are on three given circles.

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1662IMO Shortlist 1985 problem 211
1678IMO Shortlist 1986 problem 150
1710IMO Shortlist 1988 problem 30
1722IMO Shortlist 1988 problem 150
1730IMO Shortlist 1988 problem 230
1737IMO Shortlist 1988 problem 300