In and circum

Geometry Level 2

A regular polygon has an inscribed circle or radius r r and a circumscribed circle of radius R R .

If r R = cos ⁡ 1 ∘ \dfrac{r}{R}=\cos{1^{\circ}} , how many sides does the polygon have?

720 359 180 360 90

Jeremy Galvagni by Jeremy Galvagni , 48, USA

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1 solution

Jeremy Galvagni
Oct 26, 2018

cos ⁡ θ = r R \cos{\theta}=\frac{r}{R} , therefore the central angle is 2 θ = 2 ∘ 2\theta = 2^{\circ} and the polygon has 360 2 = 180 \frac{360}{2}=\boxed{180} sides.

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