1989 AIME Problems/Problem 9

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Problem

Let $a_{}^{}$, $b_{}^{}$, $c_{}^{}$ be the three sides of a triangle, and let $\alpha_{}^{}$, $\beta_{}^{}$, $\gamma_{}^{}$, be the angles opposite them. If $a^2+b^2=1989^{}_{}c^2$, find

$\frac{\cot \gamma}{\cot \alpha+\cot \beta}$

Solution

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