If a triangle \( \mathrm{ABC} \), inscribed in a fixed circle, be s...

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