| Version current |
Version 4 |
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| We describe here, informally, a limiting case of Morley's theorem. |
We describe here, informally, a limiting case of Morley's theorem. |
| \includegraphics{morley2} |
\includegraphics{morley2} |
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| One of the vertices of the triangle $ABC$, namely $C$, has been pushed |
One of the vertices of the triangle $ABC$, namely $C$, has been pushed |
| off to infinity. Instead of two segments $BC$ and $CA$, plus |
off to infinity. Instead of two segments $BC$ and $CA$, plus |
| two trisectors between them, we now have four parallel and equally |
two trisectors between them, we now have four parallel and equally |
| spaced lines. The triangle $PQR$ is still equilateral, and the three |
spaced lines. The triangle $PQR$ is still equilateral, and the three |
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triangles adjacent to it are still isosceles, but one of those has become
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triangles adjacent to it are still isoscoles, but one of those has become
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| equilateral. We have |
equilateral. We have |
| $$AQ\cdot BR = AR\cdot BP\;.$$ |
$$AQ\cdot BR = AR\cdot BP\;.$$ |
