Cotangent Trigonometry

Geometry Level 4

In $$\triangle{ABC}$$, $$BC=a \text{ cm}, AC=b \text{ cm},$$ and $$AB=c \text{ cm}.$$ Given that $$\frac{a^2+b^2}{c^2}=2011$$, find the value of

$\frac{\cot C}{\cot A+\cot B}.$

This problem is not original.

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