Problem:
Real numbers and are chosen with such that no triangle with positive area has side lengths , and or , and 1 . What is the smallest possible value of ?
Answer Choices:
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Solution:
There is a triangle with side lengths , and if and only if . There is a triangle with side lengths , and 1 if and only if , that is, . Therefore there are no such triangles if and only if . The smallest possible value of satisfies , or . The solution with is . The corresponding value of is .
The problems on this page are the property of the MAA's American Mathematics Competitions