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Q: Do three lines that intersect at the same point have to be at the same plane?

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collinear plane

no

No, only three lines can intersect at a single point.

It's possible, but for any three lines in the same plane, there could be ether one point of intersection (unlikely) or three (more probably).

No. Any pair of the three will describe a plane, so the three possible pairs describe three planes.

concurrent

its the point of concurrency

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concurrent (for geometry)

Three or more straight lines in a plane such that they intersect pairwise.

Yes, in Euclidean geometry, an infinite number of lines can meet at one point.

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