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Math Help - more circle questions

  1. #1
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    Smile more circle questions

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  2. #2
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    Hello, dgenerationx2!

    Here's #19 . . .


    19. AB is tangent to the circle and AC is a secant.

    . . AD = 4,\;AC = 9. . Find AB.
    Code:
                    B        x
                  * * * - - - - - - * A
              *           *       /
            *               *   / 4
           *                 * D
                            /
          *               /   *
          *             /     *
          *           / 5     *
                    /
           *      /          *
            *   /           *
              *           *
            C     * * *
    Let AB = x.

    Theorem:
    If a tangent and a secant are drawn to a circle from an external point,
    the tangent is the mean proportional between the external segment
    of the secant and the entire secant.

    Hence: . \frac{AB}{AD} \:=\:\frac{AC}{AB} \quad\Rightarrow\quad \frac{x}{4} \:=\:\frac{9}{x} \quad\Rightarrow\quad x^2 \:=\:36

    Therefore: . x \:=\:6

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