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Answer to Question #300 in Geometry for kimb

Question #300
Can the line, which doesn’t contain any of triangle’s vertices, intersect all sides of this triangle? Why?
Expert's answer
Yes, it can. If there is such line and it intersects all sides of the triangle, each two vertices are placed in different half-planes. The triangle has three vertices, so there are must be at least three half-planes. But according to the fourth Euclid's axiom a line divides the plane into two half-plane only. So, we get the contravention.

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