# Answer to Question #290 in Geometry for Jessy

Question #290
There is a line and three points (A, B and C), which do not belong to this line. The segment AB intersects the line, and the segment AC doesn&rsquo;t intersect it. Does the segment BC intersects the line or it doesn&rsquo;t?
1
2010-06-14T06:29:51-0400
According to fourth Euclid&#039;s axiom a line divides the plane into two half-plane. Call these half-plane X and Y. Let the point A belong to the half-plane X. The segment AB intersects the line, thus the point B doesn&rsquo;t belong to the half-plane X, so it belongs to the half-plane Y. The segment AC doesn&rsquo;t intersect the line thus the points A and C belongs to the same half-plane &ndash; the half-plane X. We get: the point B belongs to the half-plane Y, point C belongs to the half-plane X, so the ends of the segment BC belongs to different half-planes; thus the segment BC intersects the line.

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