Given a circle and two points on that circle, P and Q, draw the chord PQ, and label its midpoint M.

Now draw two other chords of the circle AB and CD that both pass through M.

Further, draw chords AD and BC.

Label the intersection of AD and PQ, point X.
Label the intersection of BC and PQ, point Y.
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Prove that M is the midpoint of line segment XY.

(In reply to re(4): stumper -- A Visual Guess by Thalamus)

You are quite wrong, and you have certainly not put me in a forgiving mood. I challenge you to try only words from the problem description and thereby find "butterfly problem."  At any rate, it is really unimportant how I found "butterfly problem" -- I found it, but I didn't solve it, and I doubt that you could even have found it, let alone solve it yourself. The point is that it is a hard problem with a considerable history, independent of your ignorant opinions of my veracity. 

Posted by Richard on 2004-03-26 16:57:53