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(3): stumper -- A Visual Guess by Richard)

You'll forgive me, I hope, if I doubt the veracity of your statement that "butterfly" occured to you, out of the blue.

Once you found a reference to the "butterfly theorem", I'm sure you are correct that "adding butterfly really does" zero in better on an existing web solution.

Posted by Thalamus on 2004-03-26 16:25:22