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Math Help - Circle Geometry

  1. #1
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    Circle Geometry

    23. Two circles intersect at A and B. The tangent to the first cirlce at A cuts the second circle at c and the tangent to the second circle at A cuts the first circle at D. Prove that Tri ABC and Tri DBA are similar.

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  2. #2
    MHF Contributor red_dog's Avatar
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    For the first circle:

    \left\{\begin{array}{ll}m(\widehat{DAB})=\frac{arc  (AB)}{2}\\<br />
m(\widehat{ACB})=\frac{arc(AB)}{2}\end{array}\righ  t.\Rightarrow \widehat{DAB}=\widehat{ACB}

    For the second circle:

    \left\{\begin{array}{ll}m(\widehat{BAC})=\frac{arc  (AB)}{2}\\<br />
m(\widehat{ADB})=\frac{arc(AB)}{2}\end{array}\righ  t.\Rightarrow \widehat{BAC}=\widehat{ADB}
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