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Berkeley Math Circle Monthly Contest 1

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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