Centroids with medial triangle

Below is a triangle and it's medial triangle.
Compare the centroids of triangle ABC and the centroids of the triangles formed by the sides of the medial triangles and the parts of the original.
What do you notice about the centroids?

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Focus on B', G, Gb, and B:
How do their lengths compare?
What are the ratios to get from one to another?

Christy Bredestege, Created with GeoGebra