A degenerate case of Pascal's theorem (four points) is interesting; given points ABCD on a conic Γ, the intersection of alternate sides, AB ∩ CD, BC ∩ DA, together with the intersection of tangents at opposite vertices (A, C) and (B, D) are collinear in four points; the tangents being degenerate 'sides', taken at two possible positions on the 'hexagon' and the corresponding Pascal line sharing either degenerate intersection. This can be proven independently using a property of pole-polar. If the conic is a circle, then another degenerate case says that for a triangle, the three points that appear as the intersection of a side line with the corresponding side line of the Gergonne triangle, are collinear.