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Math Help - [SOLVED] Prove that BP ll AQ.. circle geometry. HELP!!!

  1. #1
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    [SOLVED] Prove that BP ll AQ.. circle geometry. HELP!!!

    Two unequal circles intersect at P & Q. PA is a tangent to the larger circle and a chord of the smaller one, while QB is a tangent to the smaller circle and a chord of the larger one. Prove that BP is parallel to AQ.

    http://i420.photobucket.com/albums/p...tcheese/Q8.jpg

    I've gotten the diagram but I don't know how to prove it. I know all my circle properties, but I can't see through this for some reason!

    It would be greatly appreciated if someone could help me solve this.

    Thanks
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  2. #2
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    The angles QBP and QPA are equal by the alternate segment theorem for the larger circle. The angles QPA and AQC are equal by the alternate segment theorem for the smaller circle, where C is on the line BQ on the opposite side of Q from B.

    Therefore the angles QBP and CQA are equal, which makes the lines AQ and BP parallel.

    [You can find the statement and proof of the alternate segment theorem here. Scroll down towards the bottom of the page.]
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