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.

Centroid of

A

Circumcenter of

A

Incenter of

A

Orthocenter of

A

Circumcenter of

B

Incenter of

B

Orthocenter of

B

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