# Empty Triangle!

Geometry Level 2

The center of gravity of a solid triangle is the point where its medians intersect (its centroid).

Consider a hollow triangle, $$A,$$ whose sides are made of uniformly dense, thin strings. Let $$B$$ be the triangle formed by connecting the midpoints of $$A.$$

Where is the center of gravity of $$A?$$

For reference, here are the other three common triangle centers: circumcenter, incenter, and orthocenter.

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