Q: Which can be the intersection of two distinct lines?

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yes

If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.

If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 6 points of intersection.

Six (6)

In Euclidian geometry it's a point. In non-Euclidean geometry all bets are off.

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yes

discuss the possible number of points of interscetion of two distinct circle

If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.

If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 6 points of intersection.

If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 499500 points of intersection.

The intersection of two distinct planes is a line. The set of common points in the line lies in both planes.

Six (6)

If two distinct planes intersect, therefore their intersection is a line.

A line

In Euclidian geometry it's a point. In non-Euclidean geometry all bets are off.

A line or edge.

point