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

Fair enough.  I offer my apology.

I'm sorry you have a tendency to search for answers on the internet rather than attempt to solve the problems yourself.  And I'm sorry that you then add "butterfly" to it, to make the seach more narrow.  And I further commend you on your facility with the google search engine.

Lastly, I thank you for accepting my apology.

Posted by Thalamus on 2004-03-27 00:18:04