CEMC Hypatia, 2009

Geometry Difficulty 3.0 AMC 10/12 Prove it Canada

A solid right prism $ABCDEF$ has a height of $16$ , as shown. Also, its bases are equilateral triangles with side length $12$ . Points $X$ , $Y$ , and $Z$ are the midpoints of edges $AC$ , $BC$ , and $DC$ , respectively. Determine the lengths of $XY$ , $YZ$ and $XZ$ .

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