What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm?
- A. 1+\sqrt{2}cm
- B. 2+\sqrt{2}cm
- C. 2+\sqrt{3}cm ✓
- D. 3+\sqrt{3}cm
Correct Answer: C. 2+\sqrt{3}cm
Explanation
For a regular polygon with n sides and side length a, the radius of the inscribed circle is r = \frac{a}{2} \cot(\frac{\pi}{n}). Here n = 12 and a = 1. The radius is r = \frac{1}{2} \cot(15^\circ). The diameter is d = 2r = \cot(15^\circ) = 2+\sqrt{3} cm.