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 CorollaryOfMorleysTheorem 2013-03-22 13:46:22 2013-03-22 13:46:22 drini (3) drini (3) 8 drini (3) Corollary msc 51M04