Pascal's Thoerem

If six points A, B, C, D, E, F are on a circle,
then the intersection point of AB and DE,
the intersection point of BC and FE and
the intersection point of CD and FA are on a line.

You can move six points on the above circle using mouse.

Extended Pascal's Thoerem.

Let n be an integer greater than 3.
If 2n points A1, A2, ..., A(2n) are on a circle,
then n(n-2) intersection points of A(2i-1)A(2i) and A(2j)A(2j+1) 　(0 < i < n+1, 0 < j < n+1, i =/ j, A(2n+1) = A1)
are on a curve of degree n-2.

n = 4

n = 5