If a \( \triangle A B C \), inscribed in a fixed circle, is slightly varied in such a way as to ...

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If a \( \triangle A B C \), inscribed in a fixed circle, is slightly varied in such a way as to have its vertices always on the circle, show that \( \frac{d a}{\cos A}+\frac{d b}{\cos B}+\frac{d c}{\cos C}=0 \).
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