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Equilateral triangles with vertices in circles

Source: Romanian IMO TST 2006, day 2, problem 2

April 22, 2006
geometryinequalitiesromania

Problem Statement

Let ABCABC be a triangle with ∠B=30∘\angle B = 30^{\circ }. We consider the closed disks of radius AC3\frac{AC}3, centered in AA, BB, CC. Does there exist an equilateral triangle with one vertex in each of the 3 disks?
Radu Gologan, Dan Schwarz
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