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.
_____________________________

Prove that M is the midpoint of line segment XY.

(In reply to re(6): stumper -- A Visual Guess by Thalamus)

It seems to me that one who is so quick to accuse another of being untruthful must in fact think that everyone else must be a big liar because he himself is.  I don't intentionally give misinformation in my comments here on perplexus, and can see little reason why a person would.  It  is extremely impolite to call someone a liar in your comments here, even if that is what you really think.  And since I have answered you in no uncertain terms that what I wrote about my perception of the  "butterfly" figure was in fact completely true, politese requires you to give me an apology, not derision such as "Methinks thou dost protest too much.  ;-)."  Your apology is accepted in advance, should you ever offer it, and I intend to comment no further on this.

Posted by Richard on 2004-03-26 23:01:06