Given a nonequilateral triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
, the vertices listed counterclockwise, find the locus of the centroids of the equilateral triangles
![A'B'C'](/media/m/5/3/d/53d1d147ad89bd52a7038ce57a0957ef.png)
(the vertices listed counterclockwise) for which the triples of points
![A,B', C'; A',B, C';](/media/m/9/2/d/92d2d0679bcef28d541c213b4766ff14.png)
and
![A',B', C](/media/m/d/e/e/deea97ad50dbcc7d5efaa72f9e050267.png)
are collinear.
Proposed by Poland.
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Given a nonequilateral triangle $ABC$, the vertices listed counterclockwise, find the locus of the centroids of the equilateral triangles $A'B'C'$ (the vertices listed counterclockwise) for which the triples of points $A,B', C'; A',B, C';$ and $A',B', C$ are collinear.
Proposed by Poland.