Thomsen's Figure

Take any Triangle with Vertices $A$, $B$, and $C$. Pick a point $A_1$ on the side opposite $A$, and draw a line Parallel to $AB$. Upon reaching the side $AC$ at $B_1$, draw the line Parallel to $BC$. Continue (left figure). Then $A_3=A_1$ for any Triangle. If $A_1$ is the Midpoint of $BC$, then $A_2=A_1$ (right figure).

See also Midpoint, Triangle

References

Madachy, J. S. Madachy's Mathematical Recreations. New York: Dover, pp. 234, 1979.