TriangleConicTheorem
A theorem about triangles and conics from http://www.cut-the-knot.org/m/Geometry/BuratinoPascal.shtml
For any triangle ABC, let P be a point in its interior. Define six points on the triangle as follows:
For each side of the triangle, consider the line passing through P which is parallel to that side; two of the desired points are the intersection of that line with each of the other sides.
Then those six points all lie on the same conic (ie, ellipse, parabola, or hyperbola).