# 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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