Let $P_1,..,P_n$ be $n$ points in plane such that every line $P_i P_j$ contains another $P_k$. Show that the given points are collinear.
2026-03-27 07:12:02.1774595522
Collinearity condition in plane
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Hint. By the Sylvester–Gallai theorem, given a finite number of points in the plane, either all the points are collinear or there is a line which contains exactly two of the points.