Divide a triangle by its three medians into six smaller triangles. Surprisingly, the circumcenters , , etc. of the six circumcircles
of these smaller triangles (shown in blue above) are concyclic.
Their circumcircle (shown in green above) is known as the van Lamoen circle.
Li, K. Y. "Concyclic Problems." Math. Excalibur, 6-1, 1-2, 2001. http://www.math.ust.hk/excalibur/v6_n1.pdf.Myakishev,
A. and Woo, P. "On the Circumcenters of Cevasix Configurations." Forum
Geom.3, 57-63, 2003. http://forumgeom.fau.edu/FG2003volume3/FG200305index.html.van
Lamoen, F. "Problem 10830." Amer. Math. Monthly107, 863,
2000.van Lamoen, F. "Solution to Problem 10830." Amer.
Math. Monthly109, 396-397, 2002.