Nine Point cirlce of a triangle

1 | ```
NinePointCircle(P1, P2 = c(0, 1), P3 = c(1, 0), add = FALSE, SHOW = TRUE)
``` |

`P1` |
vector, Point 1 |

`P2` |
vector, Point 1 |

`P3` |
vector, Point 1 |

`add` |
add to existing plot |

`SHOW` |
create a new plot and add |

circle passes through nine points that can be calculated for any triangle. Also known as Feuerbach's circle, Euler's circle, Terquem's circle, the six-point circle, the twelve-point circle, the n-point circle, the medioscribed circle, the mid circle, the circum-midcircle.

list of essential points:

`A` |
2-vector, vertex point 1 |

`B` |
2-vector, vertex point 2 |

`C` |
2-vector, vertex point 3 |

`D` |
2-vector, mid-point opposite A |

`E` |
2-vector, mid-point opposite B |

`F` |
2-vector, mid-point opposite C |

`G` |
2-vector, foot altitude point opposite A |

`H` |
2-vector, foot altitude point opposite B |

`I` |
2-vector, foot altitude point opposite C |

`J` |
2-vector, mid point from S-A |

`K` |
2-vector, mid point from S-B |

`L` |
2-vector, mid point from S-C |

`S` |
2-vector, Intersection point of altitudes |

`CEN` |
2-vector, center of nine point circle |

`R` |
radius of nine point circle |

Jonathan M. Lees<jonathan.lees@unc.edu>

http://en.wikipedia.org/wiki/Nine-point_circle

TriangleInfo, TriangleCenter

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