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