Determining the Top triangle of a Pentagram

Hello genii,

I bet this will stump you,

Given 5 outer points (x,y) of a five sided star:

-23.0000 | 17.3200 |

-11.3676 | 24.2994 |

-33.3421 | 26.0574 |

-11.6912 | 16.0979 |

-17.4368 | 26.5549 |

and 5 inner points of the pentagon within it:

-18.4540 | 24.8663 |

-19.2453 | 19.5728 |

-16.4195 | 24.7036 |

-21.1226 | 20.4364 |

-15.0000 | 22.1200 |

I want to determine the outer point that is opposite the pentagon corner angle that is closest to 90 degrees. In other words, I want the outer point of the triangle that makes the pentagon resemble a diamond.

How do I do that using formulae?

Re: Determining the Top triangle of a Pentagram

Hey Stockgoblin.

Hint: The equation for a line in 2D is y = mx + b and two lines are perpendicular if m1*m2 = -1.

Now you need to just get the equations for two perpendicular lines using your constraints and solve for the m's and b's.