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 pushedoff to infinity. Instead of two segments $BC$ and $CA$, plustwo trisectors between them, we now have four parallel and equallyspaced lines. The triangle $PQR$ is still equilateral, and the threetriangles adjacent to it are still isosceles, but one of those has becomeequilateral. We have

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