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Math Help - circle, tangent

  1. #1
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    circle, tangent



    Line segment BA is tangent to the circle at A. CF is tangent to the circle at F. Express the length of DE in terms of θ.

    Thanks so much.

    I know it is 4(some identity)θ???
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  2. #2
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    Hello, daydreembelievr!



    Line segment BA is tangent to the circle at A.
    CF is tangent to the circle at F.
    Express the length of DE in terms of \theta.

    In right triangle O\cdot\sin\theta" alt="DEO\!:\;\;\sin\theta \:=\:\frac{DE}{DO} \quad\Rightarrow\quad DE \:=\O\cdot\sin\theta" />

    But DO is a radius of the circle: . DO \:=\:4

    Therefore: . DE \;=\;4\sin\theta

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