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Consider a circle $k$ with radius $2.5\mathrm{cm}$. In the circle is inscribed a convex quadrilateral $ABCD$ so that the diagonal $AC$ is the diameter of the circle, the length of $BC$ is $\sqrt{21}\mathrm{cm}$, and the length of $DC$ is $4\mathrm{cm}$. What is the length of the shortest side of this quadrilateral? (See the picture.)