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