- #1
Mr Davis 97
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Homework Statement
##ABC## is a triangle, the midpoint of ##AB## is ##H##. Prove that ##2CH < AC+CB##.
Homework Equations
The Attempt at a Solution
Note that by the triangle inequality that ##CH \le HA + AC## and that ##CH \le HB + BC##. Adding these two inequalities gives $$2CH \le HA+HB+AC+CB = AB+AC+CB < AC+CB.$$
This problem is from a problem-solving book, but it seems way too easy and uninteresting. Am I making some egregious error, or is it just easy?