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Math Help - Circle Geometry: Proving Parrallel Lines

  1. #1
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    Circle Geometry: Proving Parrallel Lines

    Two circles intersects in X and Y. The tangent at X to the first circle cuts the second circle at A and AY produced cuts the first circle at B. Prove that XB is parallel to the tangent at A to the second circle.
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  2. #2
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    Extend  AX we have X being in the segment  AM therefore ,  \angle MXB = \angle BYX Moreover , \angle NAX = \angle AYX where  AN is the tagent to the second circle and  N and B are in the opposite side .


    By looking at line  AYB we obtain

     180^o = \angle BYX + \angle AYX = \angle MXB + \angle NAX

     \angle AXB = \angle NAX
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  3. #3
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    Where is M located?

    Sorry, isnt X a tangent? Producing AX will not render M on circle.
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  4. #4
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    Ok nvm
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