## Problem of the Day #338: Albert’s Quadrilaterals
*February 20, 2012*

*Posted by Saketh in : potd , trackback*

Given any quadrilateral $ABCD$, Albert draws in the points $P$, $Q$, $R$, and $S$ – the midpoints of sides $BC$, $CD$, $DA$, and $AB$ respectively. He then determines the value of $$\frac{AP^2 + BQ^2 + CR^2 + DS^2}{AB^2 + BC^2 + CD^2 + DA^2}$$ What is the largest possible ratio Albert could find?

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