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Math Help - what is your opinion in that problem

  1. #1
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    Smile what is your opinion in that problem

    here is a picture for a problem my master asked me to solve it in the attachment
    the question is prove that c/Sin C = 2r
    here is my proof :
    Construction : draw MD perpendicular to AB chord
    Proof :
    since -->MD perpendicular to AB
    so -->MD bisects <M
    so -->Sin <BMD = opposite / hypotenuse = BD / r
    since --><M and <C two angles subtended by same arc
    so --><C = 0.5 * <M = <BMD
    so -->sin C = BD / r
    since -->BD = 0.5 * side c
    so -->sin C = (0.5*c)/r
    so -->r = (0.5*c)/sin C (multiplication the equation by 2)
    so -->2r = c / sin C and that is required to prove

    what is your opinion about this solution ???
    Attached Thumbnails Attached Thumbnails what is your opinion in that problem-untitled.jpg  
    Last edited by mido22; August 11th 2011 at 05:32 PM.
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  2. #2
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    Re: what is your opinion in that problem

    Quote Originally Posted by mido22 View Post
    here is a picture for a problem my master asked me to solve it in the attachment
    the question is prove that c/Sin C = r^2 ***
    here is my proof :
    Construction : draw MD perpendicular to AB chord
    Proof :
    since -->MD perpendicular to AB
    so -->MD bisects <M
    so -->Sin <BMD = opposite / hypotenuse = BD / r
    since --><M and <C two angles subtended by same arc
    so --><C = 0.5 * <M = <BMD
    so -->sin C = BD / r
    since -->BD = 0.5 * side c
    so -->sin C = (0.5*c)/r
    so -->r = (0.5*c)/sin C (multiplication the equation by 2)
    so -->2r = c / sin C and that is required to prove

    what is your opinion about this solution ???
    I agree with your proof that \frac{c}{\sin{C}} = 2r ... but what about \frac{c}{\sin{C}} = r^2 *** ? is that a typo?
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  3. #3
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    Re: what is your opinion in that problem

    no sry real question is 2*r not ^2
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