TITLE: Question about tangent conics
QUESTION [15 upvotes]: Suppose we have two conic section curves (the red one and the blue one) that are each tangent to a third conic (the black one) in two places. The picture shows ellipses, but I don't think that matters.

Now suppose we draw four lines as shown: two lines connecting opposite intersection points (the green ones), and two lines connecting opposite tangency points (the pink ones).
It appears that the four lines meet at a point. Is that true? Is this a known result, and, if so, does it have a name? Proof or reference, please?

REPLY [8 votes]: I just found this, which I'm currently struggling to understand. It's on page 287 of "THE PRINCIPLES OF PROJECTIVE GEOMETRY APPLIED TO THE STRAIGHT LINE AND CONIC" by 
J. L. S. HATTON, Cambridge University Press, 1913.
There's a legal electronic copy here.
So, the result is known (or, at least, it was known in 1913).