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Math Help - Circle geometry

  1. #1
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    Circle geometry

    21. Two points A and b are taken on a circle and C in the other end of the diameter through A. If AE is the perpendicular from A ont ot he tangent at B, prove that AB bisects angle CAE.
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  2. #2
    MHF Contributor red_dog's Avatar
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    m(\widehat{BAC})=\frac{m(arcBC)}{2}

    m(\widehat{EBA})=\frac{m(arcAB)}{2}

    m(\widehat{EAB})=90^{\circ}-m(\widehat{EBA})=90^{\circ}-\frac{m(arcAB)}{2}=\frac{180^{\circ}-m(arcAB)}{2}=\frac{m(arcBC)}{2}

    Then m(\widehat{BAC})=m(\widehat{EAB})
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