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Math Help - Circle Question

  1. #1
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    Circle Question

    You have a circle....a chord AB is 20 inches long....the distance between the midpoint of AB and the nearest point on the circle is 5

    whats the radius?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by stones44 View Post
    You have a circle....a chord AB is 20 inches long....the distance between the midpoint of AB and the nearest point on the circle is 5

    whats the radius?
    You need the intersecting chord theorem (and a diagram).

    RonL
    Attached Thumbnails Attached Thumbnails Circle Question-gash.jpg  
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  3. #3
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    that doesnt really help

    I need to find the radius
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by stones44 View Post
    that doesnt really help

    I need to find the radius
    Pffl. It took me less than 30 seconds to google it. See here.

    -Dan
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by stones44 View Post
    that doesnt really help

    I need to find the radius
    did you look up what the intersecting chord theorem was? see here

    EDIT: Dan's site seems a lot nicer than mine

    Quote Originally Posted by stones44 View Post
    that doesnt really help

    I need to find the radius
    can you tell us what the solution is now?
    Last edited by ThePerfectHacker; June 2nd 2007 at 05:45 PM.
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  6. #6
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    Quote Originally Posted by stones44 View Post
    that doesnt really help

    I need to find the radius
    No you need to learn how to do research for yourself, you have been given
    the name or the result you need. Now it seems improbable that you have not
    covered this in class, so it will be in your notes or text book.

    Now where I come from text books have indexes, so you could try looking it
    up in the index. Also you could, as you appear to have access to the
    internet, try typing it into Google. If you don't know what Google is then
    follow this: link to Google.

    Intersecting Chord Theorem

    Let AB and CD be two chords in the same circle that intersect at a point
    X. Then:

    |AX|*|XB| = |CX|*|XD| ... (1)

    (Where |UV| denotes the length of the line segment UV.)

    Now look at the diagram I posted. Do you see two intersecting chords?
    Have I marked their lengths?

    So now label the points as in the statement of the theorem and then
    note which lengths appear in the statement of the intersecting chord
    theorem and so write (1) in terms of the lengths of these chords.

    Now solve the resulting equation for R.

    RonL
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  7. #7
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    its 15

    sorry, just wasn't thinking
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  8. #8
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    Hello, stones44!

    No fancy theorems needed . . .


    You have a circle and a chord AB is 20 inches long.
    The distance between the midpoint of AB and the nearest point on the circle is 5.
    What is the radius?
    Code:
                    C
                  * * *
              *     |5    *
            *  10   |   10  *
          A*- - - - + - - - -*B
              *     |
          *    R *  |R-5      *
          *         *         *
          *         O         *
    
           *                 *
            *               *
              *           *
                  * * *

    Let the radius be R.

    We have a right triangle with sides: R-5,\:10,\: R

    R^2\:=\:(R-5)^2+10^2\quad\Rightarrow\quad R^2 \:=\:R^2 - 10R + 25 + 100

    . . 10R \:=\:125\quad\Rightarrow\quad R\:=\:12.5

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  9. #9
    Member GAdams's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, stones44!

    No fancy theorems needed . . .


    Code:
                    C
                  * * *
              *     |5    *
            *  10   |   10  *
          A*- - - - + - - - -*B
              *     |
          *    R *  |R-5      *
          *         *         *
          *         O         *
    
           *                 *
            *               *
              *           *
                  * * *

    Let the radius be R.

    We have a right triangle with sides: R-5,\:10,\: R

    R-5)^2+10^2\quad\Rightarrow\quad R^2 \:=\:R^2 - 10R + 25 + 100" alt="R^2\:=\R-5)^2+10^2\quad\Rightarrow\quad R^2 \:=\:R^2 - 10R + 25 + 100" />

    . . 10R \:=\:125\quad\Rightarrow\quad R\:=\:12.5

    How did you get from:
    (r - 5)^2 to r^2 - 10r ?
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  10. #10
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    Hello, GAdams!

    How did you get from: (r - 5) to r - 10r ?
    Have you forgotten your basic algebra? . . . FOIL!

    . . (R - 5)^2 \;=\;(R-5)(R-5)\;=\;R^2 - 5R - 5R + 25 \;=\;R^2 - 10R + 25

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  11. #11
    Member GAdams's Avatar
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    Thanks. I wasn't paying attention.

    Excuuse: it's like Sunday today, right?
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  12. #12
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    oooh thanks
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