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Math Help - Geometry proof help please?

  1. #1
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    Geometry proof help please?

    Imageshack - circlesg.jpg

    There are two circles touching at C. The larger has midpoint B, the smaller goes through B. Prove that any chord [AB] of the circle is bisected by the smaller circle.

    I can prove that angle AEC and angle BDC are 90 degrees, and that AB:BC = 1:1

    How do I prove the rest?


    -DLA
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  2. #2
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    Quote Originally Posted by DarkLightA View Post
    Imageshack - circlesg.jpg

    There are two circles touching at C. The larger has midpoint B, the smaller goes through B. Prove that any chord [AB] of the circle is bisected by the smaller circle.

    I can prove that angle AEC and angle BDC are 90 degrees, and that AB:BC = 1:1

    How do I prove the rest?


    -DLA
    Triangle AEC and BDC are right angled triangles, and AE is parallel to BD. Since AB = BC, ED = DC. It is true for any chord.
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