Think of the edge of a coin falling on a hard wood floor as a model of this problem.
A circle (the edge of the coin in the model) and not the disk (the entire coin) of radius 1 unit falls onto a infinite plane with parallel lines spaced 1 unit apart. How many intersections (points) of the circle with the entire set of lines are there?
Per Chris Lewis' question: the circle falls flat onto the lines. It does not fall so that it stays on edge. The statement of "the edge of the coin" is to explain the difference between a circle and a disk as some people are not aware of what the difference is.
The answer is 4.
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1 solution
The circle intersects either two or four lines. The cases of zero, one, three, or more than four lines is not possible. In the case of two lines, the circle intersects each line twice: 2 × 2 = 4 . In the case of four lines, the circle touches the outer two lines once and the central line twice: 2 × 1 + 2 = 4 .