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Problem of the Day #333: Squares within Squares February 15, 2012

Posted by Alex in : potd , trackback

Square $ABCD$ has side length $1$. Albert chooses points $E$, $F$, $G$, and $H$ on sides $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DA}$ respectively, such that each point divides its segment into two parts, with lengths given by the ratio $2:3$. Points $E$, $F$, $G$, and $H$ are closer to points $A$, $B$, $C$, and $D$ respectively. Find the area of square $EFGH$.


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