Triangle Medians

This triangle has vertices $A_0$, $A_1$ and $A_2$. The points $M_0$, $M_1$ and $M_2$ are, respectively, the midpoints of the sides opposite $A_0$, $A_1$ and $A_2$. In the interactive pop-up the blue points $A_0$, $A_1$ and $A_2$ can be dragged about with the mouse to change the triangle, but $A_0M_0$, $A_1M_1$ and $A_2M_2$ remain the medians of the resulting triangle. The red point $G$, the triangle's centroid, marks the three coincident pairwise intersections of $A_0M_0$, $A_1M_1$ and $A_2M_2$.