A geometry problem by Skanda Prasad

Geometry Level 3

Given that in a triangle \(ABC\) with side lengths \(a\), \(b\) and \(c\),

\[\begin{align} \cot\dfrac{A}{2} \cot\dfrac{B}{2} & =c \\ \cot\dfrac{B}{2} \cot\dfrac{C}{2} & =a \\ \cot\dfrac{C}{2} \cot\dfrac{A}{2}& =b \end{align} \]

Find the value of \(\dfrac{1}{s-a}+\dfrac{1}{s-b}+\dfrac{1}{s-c}\), where \(s=\dfrac{a+b+c}{2}\).

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