A line can be specified in trilinear coordinates by parameters such that the trilinear coordinates obey
(1)
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The trilinear line at infinity of a triangle with side lengths , , and is
(2)
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The line passing through points and is given by
(3)
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(4)
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(5)
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Three trilinear points , , and are collinear if
(6)
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Three lines
(7)
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(8)
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(9)
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concur iff
(10)
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in which case the point of concurrence is
(11)
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