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Math Help - Circle Geometry

  1. #1
    Senior Member
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    Unhappy Circle Geometry

    Hi

    AB and AC are equal chords of a circle. AM and BN are parallel chords through A and B respectively. Prove that AN is parallel to CM.

    I've tried to prove angles NAM and AMC are equal but failed miserably. Could someone please help me with this question?

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  2. #2
    MHF Contributor red_dog's Avatar
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    m(\widehat{ABC})=m(\widehat{ACB})
    m(\widehat{ABC})=m(\widehat{AMC})=\frac{m(arcAC)}{  2}
    Then m(\widehat{AMC})=m(\widehat{ACB})=\frac{m(arcAB)}{  2}=\frac{m(arcAN)+m(arcNB)}{2}

    m(\widehat{NAB})=\frac{m(arcNB)+m(arcBM)}{2}

    But AM\parallel BN\Rightarrow m(arcAN)=m(arcBM)

    Then m(\widehat{NAB})=\frac{m(arcAB)}{2}=m(\widehat{AMC  })
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