Shao-Cheng Liu, The symmedian point and concurrent antiparallel images,
Forum Geometricorum,  9 (2009) 149--154.

Abstract:  In this note, we study the condition for concurrency of the GP lines of the three  triangles determined by three vertices of a reference triangle and six vertices of  the second Lemoine circle. Here G is the centroid and P is arbitrary triangle center different from G. We also study the condition for the images of a line  in the three triangles bounded by the  antiparallels through a given point to be concurrent.

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