Pascal's Theorem states that the opposite intersects of a circular hexagon are linear.
Imagine a light above the center of the outer circle(towards the viewer if on screen)This light projects the image onto a surface that is parallel to the plane containing the light and the (red) intersect line.
The effect of this is to move the intersect line to infinity and make the opposite intersect lines into parallels. To prevent the image from being moved off screen I have stretched,resized and moved it so that the outer circle is the same size and position as the original outer circle.
A great link from Hungary
Eric W. Weisstein. "Poncelet's Porism." From MathWorld--A Wolfram Web Resource.
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