Let \(AB\) be a diameter of a circle and let \(C\) be a point on \(AB\) with \(2 \cdot AC = BC\). Let \(D\) and \(E\) be points on the circle such that \(DC \perp AB\) and \(DE\) is a second diameter. What is the ratio of the area of \(\triangle DCE\) to the area of \(\triangle ABD\)? The original answer is in \(\frac{k}{m}\) format, please give the value of \(k + m\).

Let's think step by step and output the final answer within \boxed{}.
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