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How many planes contain the same three collinear points?
Infinitely many planes may contain the same three collinear points if the planes all intersect at the same line.
Can a plane contain one point of a line?
Yes, it can. A plane can contain any number of points of a line.
Does a plane contain at least three lines?
Yes- planes contain infinitely many points and every pair of points in plane determine a line in that plane, so every plane contains infinitely many lines.
Can a circle pass through three points of a straight line?
No, a circle can never pass through three points of a straight line. The circle will touch 1) no points of the line, 2) one point of the line (which is now tangent to the circle), or 3) two points of the line. A line can contain (at most) twopoints that lie on the line.
Can line segments have holes or missing pieces?
No it cannot because a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. If it has holes it does not contain every point between the end points.
