The above applet calculates the positions of various centres of a
reference triangle ABC, and additionally plots these relative to the disc
of diameter OSym (the disc enclosed by the Brocard circle). It is offered
to lend weight to the hypotheses advanced (generally without mathematical
proof) in section 4 of my report *"Applications of the GPAT to triangle
geometry"*, which you can find more about here.

The points are as follows:

Icon | Object | Label |

Black point | Circumcentre | O |

Dark red point | Symmedian point | Sym |

Red point | Centroid | G |

Blue point | Gergonne point | Ge |

Green point | Incenter | I |

Orange point | Mittenpunkt | M |

Grey points | Isodynamic points | S and S' |

Grey Circle | Circle of diameter OSym (Brocard circle) | D_{OSym} |

Red Circle | Circle of diameter OG | D_{OG} |

Purple Circle | Parry circle | P |

Applet development in Cinderella