[alogo] Cosymmedian triangle

Triangle DEF is the cosymmedian triangle of ABC. Its vertices D, E, F are the intersections of the symmedians of ABC with the circumcircle c of ABC. K is the symmedian or Lemoine point of triangle ABC. Triangles ABC and DEF share the same Lemoine point K, same Brocard circle with diameter OK, circumcircle c, Lemoine axis A*B*C*, Brocard axis (line [OK]), isodynamic points and Apollonian circles.

[0_0] [0_1] [0_2] [0_3]
[1_0] [1_1] [1_2] [1_3]
[2_0] [2_1] [2_2] [2_3]

All these are consequences of the fact that the cosymmedian triangle is an orbit of the (Moebius) Recycler of ABC. This is studied in Recycler.html .

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