Concurrent
Two or more lines are said to be concurrent if they intersect in a single point. Two lines concur if their trilinear coordinates satisfy
Three lines concur if their trilinear coordinates satisfy
l_1alpha+m_1beta+n_1gamma =
(2)
l_2alpha+m_2beta+n_2gamma =
(3)
l_3alpha+m_3beta+n_3gamma = 0,
(4)
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
A_1x+B_1y+C_1 =
(6)
A_2x+B_2y+C_2 =
(7)
A_3x+B_3y+C_3 = 0.
(8)
are concurrent if their coefficients satisfy
See also
Concyclic, PointExplore with Wolfram|Alpha
WolframAlpha
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Cite this as:
Weisstein, Eric W. "Concurrent." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Concurrent.html