- #1

Derrida

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It is well known by Varignon's Theorem and the Triangle Inequality that in a convex quadrilateral ABCD with midpoints a of side AB, b of side BC, ... d of side DA and perimeter p,

\[ AC + BD < p\]

where AC and BD are the diagonals of the quadrilateral. However, how do I obtain the lower bound to this inequality, namely that

\[ \frac{p}{2} < AC + BD \]

I'm not looking for answers to this question, only ideas that help guide me to the solution of this problem. Thanks very much.

Sorry I'm not very familiar with the latex commands in this forum, I tried enclosing [itex] [/itex] around my formulas but something funny appears (Both display just AC + BD < like that).