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parameters for cosine of angles in a triangle sum up to 2
Posted: Sun Feb 08, 2015 10:58 pm
by Masum
For a triangle $\Delta ABC$, prove that there are real numbers $s_A,s_B,s_C$ so that,
$1. 0<s_A,s_B,s_C<1$
$2. s_A+s_B+s_C=2$
$3. s_A\cos A+s_B\cos B+s_C\cos C=1$
Re: parameters for cosine of angles in a triangle sum up to
Posted: Mon Feb 09, 2015 12:27 pm
by *Mahi*
Hint:
$\color{white}{\text{Draw a perpendicular from any vertex to the opposite side.}}$ $\color{white}{\text{ Does the division remind you of something?}}$
Re: parameters for cosine of angles in a triangle sum up to
Posted: Tue Feb 10, 2015 7:06 pm
by Masum
Well, I created this using the same method but I was hoping for a solution with Barycentric coordinate system.
