parameters for cosine of angles in a triangle sum up to 2

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Masum
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parameters for cosine of angles in a triangle sum up to 2

Unread post by Masum » Sun Feb 08, 2015 10:58 pm

For a triangle $\Delta ABC$, prove that there are real numbers $s_A,s_B,s_C$ so that,
$1. 0<s_A,s_B,s_C<1$
$2. s_A+s_B+s_C=2$
$3. s_A\cos A+s_B\cos B+s_C\cos C=1$
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*Mahi*
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Re: parameters for cosine of angles in a triangle sum up to

Unread post by *Mahi* » Mon Feb 09, 2015 12:27 pm

Hint:

$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$
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Masum
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Re: parameters for cosine of angles in a triangle sum up to

Unread post by Masum » Tue Feb 10, 2015 7:06 pm

Well, I created this using the same method but I was hoping for a solution with Barycentric coordinate system. :)
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