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MathWorld
If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.
$\triangle ABC$内接于二次曲线, 直线$BC$上一点$D$的极线交$CA,AB$于$E,F$, 则$E,F$对偶.
[证明]
$\triangle DEF$是自极三角形, 所以$DE$是$F$的极线.
| Harold Scott Macdonald Coxeter, Projective geometry, Springer (2003)
8.31 |
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