2010012901

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2010012901
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Consider a circle \( k \) with radius \( 5\,\mathrm{cm} \). 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 \( 8\,\mathrm{cm} \), and the length of \( DC \) is \( 5\,\mathrm{cm} \). Determine the length of side \( AD \). (See the picture.)
\(5 \sqrt{3}\,\mathrm{cm} \)
\( 8\,\mathrm{cm} \)
\( 10\,\mathrm{cm} \)
\(3 \sqrt{5}\,\mathrm{cm} \)