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: stumper -- A Visual Guess by Richard)

B.S.... that you thought it "looked a lot like a butterfly"... but very good googling on smaller phrases in the puzzle!  I see from some of your earlier comments that you are an expert googler.  ;-)

Posted by Thalamus on 2004-03-26 14:09:05