in triangle ABC if (acosA+bcosB+ccosC)/(asinB+bsinC+csinA)=(a+b+c)/9R where R is circumradius then prove that the triangle is equilateral
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i thick we should use the independant values of cos A cos B etc
Originally Posted by prasum in triangle ABC if (acosA+bcosB+ccosC)/(asinB+bsinC+csinA)=(a+b+c)/9R where R is circumradius then prove that the triangle is equilateral One way to go about it is to obtain expressions for and where is the incircle radius. If you draw perpendicular lines from the incentre to all 3 sides, then Therefore, if then and is 18 times the triangle area. Therefore and so the triangle is equilateral.
Originally Posted by Archie Meade One way to go about it is to obtain expressions for and where is the incircle radius. If you draw perpendicular lines from the incentre to all 3 sides, then Therefore, if then and is 18 times the triangle area. Therefore and so the triangle is equilateral. thanks
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