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MathNet 2013 Question 63

Math Olympiad Vault · MathNet 2013

Question 63

a) Three of six segments (four sides and two diagonals of an isosceles trapezoid) are painted red, and three others are painted green.
Prove that one can construct a triangle using the segments of the same color as its sides.

b) Is the previous statement true if these six segments are four sides and two diagonals of an arbitrary trapezoid?