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Math Help - radius of circle

  1. #1
    Member Veronica1999's Avatar
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    radius of circle

    A point P is outside a circle and is 13 inches from the center. A secant from P cuts the circle at Q and R so that the external segment of the secant PQ is 9 inches and QR is 7 inches. The radius of the circle is :


    Please help!
    I don't get the problem.

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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by Veronica1999 View Post
    A point P is outside a circle and is 13 inches from the center. A secant from P cuts the circle at Q and R so that the external segment of the secant PQ is 9 inches and QR is 7 inches. The radius of the circle is :


    Please help!
    I don't get the problem.
    1. Draw a sketch.

    2. You are dealing with 2 right triangles. Use the Pythagorian theorem:

    \left|\begin{array}{rcl}r^2&=&(3.5)^2+h^2 \\ h^2 +(3.5+9)^2&=&13^2\end{array}\right.

    Solve for h and r.
    Attached Thumbnails Attached Thumbnails radius of circle-sekradpyth.png  
    Last edited by earboth; June 19th 2010 at 10:10 PM.
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  3. #3
    Member Veronica1999's Avatar
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    Quote Originally Posted by earboth View Post
    1. Draw a sketch.

    2. You are dealing with 2 right triangles. Use the Pythagorian theorem:

    \left|\begin{array}{rcl}r^2&=&(3.5)^2+h^2 \\ h^2 +(3.5+9)^2&=&13^2\end{array}\right.

    Solve for h and r.

    You are awesome!!!!!
    Thanks.

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  4. #4
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    Hi Ronsy,

    After studying Earboth's sketch for a while, I realized there is another way to solve it. You can use the rates of the sides.

    16/13+r = 13-r/9

    Vicky.
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