# Will that be a constant?

Geometry Level 4

Let $$\Gamma$$ be a circle with radius $$r$$. Let $$A$$ be any point on $$\Gamma$$ and let $$t$$ be the tangent to $$\Gamma$$ at point $$A$$. Let $$B$$ and $$C$$ be points of $$t$$ on opposite sides of $$A$$ such that $$AB = 12r$$ and $$AC = 24r$$. Let $$P$$ be any point of $$\Gamma$$ different from $$A$$. Find the value of:

$\large{\dfrac{1}{\cot \angle APB +\cot \angle APC}}$

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