What is the diameter of a circle inscribed in a regular polygon of 15 sides with side length unity?
- A. 0\cdot5 \cot 12^{\circ}
- B. \cot 12^{\circ} ✓
- C. 0\cdot5 \tan 12^{\circ}
- D. \tan 12^{\circ}
Correct Answer: B. \cot 12^{\circ}
Explanation
The radius r of a circle inscribed in a regular n-sided polygon with side length a is r = \frac{a}{2} \cot(\frac{180^\circ}{n}). For n=15 and a=1, r = 0.5 \cot 12^\circ. The diameter is 2r = \cot 12^\circ.
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