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| Two Non-overlapping Triangles (Posted on 2016-11-27) |
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Choose six distinct points on a plane. Prove or disprove the statement: Unless five points are colinear then the points can be divided into two sets of three points which form non-overlapping triangles.
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Submitted by Brian Smith
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Solution:
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The statement is false due to one case: Three of the points are on the sides of the triangle formed by the other three points. (Picture a triangle and the midpoints of its three sides.) |
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