CorollaryOfMorleysTheorem 2003-07-19 02:49:07 2003-10-27 18:05:05 Corollary Morley's theorem \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{graphicx} We describe here, informally, a limiting case of Morley's theorem. \includegraphics{morley2} 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 $$AQ\cdot BR = AR\cdot BP\;.$$