2022 · Q53
What is the diameter of a circle inscribed in a regular polygon of 15 sides with side length unity?
Elementary MathematicsCircles
- A0.5 cot 12°
- Bcot 12°
- C0.5 tan 12°
- Dtan 12°
Explanation
For a regular n-gon of side s, the inradius is r = s/(2tan(π/n)); here r = 1/(2tan12°), so the diameter is 2r = cot12°. The common error is to use the circumradius formula s/(2sin(π/n)) instead of the inradius, which would give cosec12° rather than cot12°. The keyed option is B.