Multiple choice

What is the diameter of a circle inscribed in a regular polygon of 15 sides with side length unity?

  1. 0.5 cot 12°

  2. cot 12°

  3. 0.5 tan 12°

  4. tan 12°
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius r of an inscribed circle in a regular polygon with n sides and side length s is r = (s/2) * cot(180/n). Here n=15, s=1. r = 0.5 * cot(12). The diameter is 2r = cot(12).

AI explanation

For a regular polygon of n sides with side length a, the apothem (the radius of the inscribed circle) is given by r = (a/2) cot(180/n). For n = 15 and a = 1, the radius is 0.5 cot(12). The diameter is twice the radius, giving a value of cot(12). The result is cot 12 degrees.

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