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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