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[parent] corollary of Morley's theorem (Corollary)

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

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




"corollary of Morley's theorem" is owned by drini. [ full author list (2) | owner history (2) ]
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Cross-references: isosceles, adjacent, equilateral, lines, parallel, plus, segments, infinity, triangle, vertices, Morley's theorem

This is version 5 of corollary of Morley's theorem, born on 2003-07-19, modified 2003-10-27.
Object id is 4479, canonical name is CorollaryOfMorleysTheorem.
Accessed 4519 times total.

Classification:
AMS MSC51M04 (Geometry :: Real and complex geometry :: Elementary problems in Euclidean geometries)

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