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.

[Proof Cleared]

Edited on April 5, 2004, 2:07 pm

Now that I think about it, we must prove now that if YM does not equal MX, then there can be no chords CB and AD, s.t.  C-M-D, A-M-B, C-Y-B, and A-X-D.

Edited on April 5, 2004, 2:13 pm

Edited on April 5, 2004, 2:20 pm

Posted by Victor Zapana on 2004-04-05 14:02:59