Polygon inscribed in a circle
There is a picture of an inscribed n-side polygon in a circle above. I have a task as follow:
If an n-sided regular polygon is inscribed in a circle of radius r, find a relationship between θ and n. Solve this for n. Keep in mind there are 2π radians in a circle. (Use radians, not degrees.)
Everything what comes to my mind is θ = 2π/n, but I'm pretty sure, that is not correct answer. Could you help me to deal with it please?
$\endgroup$ 31 Answer
$\begingroup$Given that the inscribed polygon is regular, we can say that the angle subtended between any 2 line segments (originating from adjacent corners) at the center of the circle will be equal and since there will be $n$ unique angles totaling up to $2π$, each of them will be equal to $\frac{2π}{n}$.
Your answer is correct and $θ=\frac{2π}{n}$.
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