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Geometry Difficulty 3.8 AMC 10/12 Prove it United States
Problem:
Let ABCDE be a convex pentagon with perimeter 1. Prove that triangle ACE has perimeter less than 1.
Solution
Solution:
By the triangle inequality, we have AC<AB+BC and CE<CD+DE, so AC+CE+EA<AB+BC+CD+DE+EA as desired.
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