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Math Help - Two touching circles...

  1. #1
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    Two touching circles...

    Fig. shows circles which are just touching. Find x by using pythagoras theorem.

    I believe they're tangential circles.

    Here's the figure:


    p.s. i am a bit bad at drawing on pc. :P
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  2. #2
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    You mean something like



    ?

    Being both externally tangent, try to prove a more general result: let r,R be the radii of the circles, then x=2\sqrt{r\cdot R}\,.
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  3. #3
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    Uhh, no. More like this:



    and they're forcing me to use pythogoras theorem somehow
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  4. #4
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    Sorry for not being able to easily super/sub script in paint. =)

    Edit: Oops, that's supposed to be 25+7.5 for A.
    Last edited by Nyoxis; March 21st 2008 at 10:58 AM.
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  5. #5
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    Ahh, stupid me. I wasn't getting how to get that B, and now it's all clear. Thanks
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  6. #6
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    It regrettable that you did not pickup on Krizalid’s suggestion.
    I do not think that he misunderstood the x (though I wish he had used say y).
    That is the horizontal distance between the centers in terms of the radii: 2\sqrt {Rr} .
    Now the x in the original problem is R + 2\sqrt {Rr}  + r = \left( {\sqrt R  + \sqrt r } \right)^2 .
    That is an elegant formula.
    Note: \left( {\sqrt {25}  + \sqrt {7.5} } \right)^2  = {\rm{59}}{\rm{.8861278752583}}
    Last edited by Plato; March 21st 2008 at 02:06 PM.
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  7. #7
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    After being able to solve few similar problems, I'm stuck again on a problem of somewhat similar nature.

    I can't seem to comprehend this circles tangent thing I assume. Here I have to find h using pythagoras theorem again.

    Attached is the image of circles.
    Attached Thumbnails Attached Thumbnails Two touching circles...-circles_again.jpg  
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  8. #8
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    Here ya go:
    Last edited by Nyoxis; July 20th 2010 at 06:30 PM.
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