# corollary of Morley’s theorem

We describe here, informally, a limiting case of Morley’s theorem.

One of the vertices of the triangle $ABC$, namely $C$, has been pushed
off to infinity. Instead of two segments $BC$ and $CA$, plus
two trisectors between them, we now have four parallel^{} and equally
spaced lines. The triangle $PQR$ is still equilateral, and the three
triangles adjacent^{} to it are still isosceles, but one of those has become
equilateral. We have

$$AQ\cdot BR=AR\cdot BP.$$ |

Title | corollary of Morley’s theorem |
---|---|

Canonical name | CorollaryOfMorleysTheorem |

Date of creation | 2013-03-22 13:46:22 |

Last modified on | 2013-03-22 13:46:22 |

Owner | drini (3) |

Last modified by | drini (3) |

Numerical id | 8 |

Author | drini (3) |

Entry type | Corollary |

Classification | msc 51M04 |