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Chords and Chords (Posted on 2004-03-24) Difficulty: 4 of 5
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.

No Solution Yet Submitted by SilverKnight    
Rating: 3.7500 (8 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts Replies and thoughts | Comment 3 of 23 |
(In reply to No Subject by Victor Zapana)

Victor: Triangles CMY and DMX are not congruent.  You can't prove it because it's not always true.  However, you are correct that triangles CMB and AMD are similar.

Shanna: Look at the diagram a bit more.

If I recall my geometry, AM * MB = CM * CD = PM * PQ.  Maybe this will help?

I say that we draw an auxillary reflection over the diameter, and prove that the points reflect to each other.


  Posted by Tristan on 2004-03-24 18:41:15
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