Ring of Lemoine
Circles of Lemoine
Two particular cases of circles of Tücker:
First circle of Lemoine
The parallels at the sides of a triangle carried out by the not of Lemoine cut the sides in six points cocyclic.
The center O' is the medium of where O is the center of the circumscribed circle.
Lines (RQ), (ST) and (PU) are antiparallel at the sides of a triangle. The segments are of the same length and their mediums has', B' and It located on the symédianes form a triangle has' B' It homothetic of ABC in a homothety of center L.
Hexagon PQRSTU is known as hexagon of Lemoine.
Second circle of Lemoine
The antiparallel at the sides of a triangle ABC, carried out by the not of Lemoine L, cut the sides of the triangle in six points cocyclic. These points are located on the second circle of Lemoine centered in L.
The points of intersection has', B', It of right-hand sides (RQ), (ST) and (PU) are located on the symédianes.
They form a triangle has' B' It symmetrical of ABC in a symmetry of center L.
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