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Math Help - can any one help me solving this proof ???

  1. #1
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    Question can any one help me solving this proof ???

    there are more than three ways to solve this proof , but i don't know how to solve it

    a triangle m n l ,prove that :
    1/n sin L + 1/l sin M + 1/m sin N =K/A
    where K is half of the triangle's perimeter and A is the triangle's area
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  2. #2
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    Hello rana mohamed

    Welcome to Math Help Forum!
    Quote Originally Posted by rana mohamed View Post
    there are more than three ways to solve this proof , but i don't know how to solve it

    a triangle m n l ,prove that :
    1/n sin L + 1/l sin M + 1/m sin N =K/A
    where K is half of the triangle's perimeter and A is the triangle's area
    I think you want to prove
    \frac{1}{n \sin L}+\frac{1}{l \sin M}+ \frac{1}{m \sin N} = \frac{K}{A}
    Note that A = \tfrac12mn\sin L= \tfrac12ln\sin M= \tfrac12lm\sin N

    \Rightarrow \sin L = \frac{2A}{mn}, etc

    \Rightarrow \frac{1}{n \sin L}+\frac{1}{l \sin M}+ \frac{1}{m \sin N}
    =\frac{mn}{2An}+\frac{ln}{2Al}+\frac{lm}{2Am}

    =\frac{m}{2A}+\frac{n}{2A}+\frac{l}{2A}

    =\frac{l+m+n}{2A}

    =\frac{k}{A}
    Grandad
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  3. #3
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    thanx very much for helping me solving this proof
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