Concurrent (original) (raw)

Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy

|  \|l_1 m_1 n_1; l_2 m_2 n_2; l_3 m_3 n_3|=0. | (1) | | -------------------------------------------------------------------------------------------------------------------------------- | --- |

Three lines concur if their trilinear coordinates satisfy

in which case the point is

 m_2n_3-n_2m_3:n_2l_3-l_2n_3:l_2m_3-m_2l_3. (5)

Three lines

are concurrent if their coefficients satisfy

|  \|A_1 B_1 C_1; A_2 B_2 C_2; A_3 B_3 C_3|=0. | (9) | | -------------------------------------------------------------------------------------------------------------------------------- | --- |

See also

Concyclic, Point

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Cite this as:

Weisstein, Eric W. "Concurrent." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Concurrent.html

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