Move C.
The three crossings stay aligned.
Drag C, or use the slider. Only C is adjustable.
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Why it works
Pascal’s theorem
Six distinct points A–F lie on one nondegenerate conic—here, an ellipse. The three intersections of opposite sides are collinear in the projective plane whenever the construction is defined.
P = AB ∩ DE
Q = BC ∩ EF
R = CD ∩ FA
A, B, D, E, and F stay fixed. C moves on a limited arc chosen to keep all six points distinct and the three crossings finite and visible. The sides extend as dashed lines; the red line continues beyond this picture.
Every side, crossing, and line is computed from the point positions. R is calculated independently, then checked against the line through P and Q. This moving diagram illustrates the theorem; it is not a proof.