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Why is the intersection point of the diagonals of a regular polygon always the center?
Assume the center of the circumcircle is the origin. Note that a diagonal through vertex $x$ passes through the origin iff $-x$ is also a vertex iff the polygon has an even number of sides.
- 118k
2
votes
Accepted
Find the value of the interior angles of a polygon
As mentioned in my comment on StackOverflow, you can find an interior angle between three points by converting those points into vectors, and use the following known formula (for the scalar product):
$...
- 2,753
1
vote
Accepted
Area inside infinitely inscribed regular polygons
Fact 1:
Suppose a regular n-gon $S$ is inscribed inside a circle of radius $r$, then the area of $S$ is $\frac{nr^2}{2}\sin\left(\frac{2\pi}{n}\right)$ and the side length of $S$ is $2r\sin\left(\frac{...
- 340
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