Triangle $\triangle ABC$ has a right angle at $C$, $\angle A = 60^\circ$, and $AC=10$.  Find the radius of the incircle of $\triangle ABC$.
Question:
Triangle $\triangle ABC$ has a right angle at $C$, $\angle A = 60^\circ$, and $AC=10$.  Find the radius of the incircle of $\triangle ABC$.
Answer:
Let's think step by step.

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5(\sqrt{3}-1)
Triangle $\triangle ABC$ has a right angle at $C$, $\angle A = 60^\circ$, and $AC=10$.  Find the radius of the incircle of $\triangle ABC$.
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