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 Chords and Chords (Posted on 2004-03-24)
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)

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 Thoughts | Comment 7 of 23 |

This is what I can make out of the diagram initially:

angle BMC = angle AMD
angle AMC = angle BMD
triangle AMD is similar to triangle BMC
BM*MA = CM*MD = PM*MQ
PM = MQ
CY*YB = PY*YQ
AX*XD = PX*XQ

Edited on March 25, 2004, 9:05 am
 Posted by Brian Smith on 2004-03-25 09:00:56

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