Start with a circle and draw two tangent circles inside. The (black) inner tangent lines to the smaller circles intersect the large circle. The (red) lines through these intersection points are parallel to the (green) outer tangents to the small circles.
A long time ago I worked on this theorem, but I never knew the name. Without a name it's difficult to find more information. Does anyone know if this theorem has a name and where I can find more information about it?