Let M be a point inside parallelogram ABCD. Then prove that $MA + MB + MC + MD < 2(AB + BC)$
I tried this problem using Triangle Inequality but couldn't proceed. Please help.
2026-02-23 04:33:48.1771821228
Parallelogram Inequality
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Let $PP'$ be parallel to $BC$ and $QQ'$ parallel to $AB$, both through $M$. Note that you can apply the triangle inequality to $AM$, $AP'$ and $MP'$. Same for others.