show that triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.(using calculus only)

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- Jun 11th 2011, 08:13 AMayushdadhwalmaximum area
show that triangle of maximum area that can be inscribed in a given circle is an equilateral triangle.(using calculus only)

- Jun 12th 2011, 12:23 AMFernandoRevilla
This may help you:

Math Forum - Ask Dr. Math - Jun 12th 2011, 05:40 AMAlso sprach Zarathustra
Can someone check this(?):

$\displaystyle S_{ABC}=\frac{abc}{4R} $ is the area of triangle inscribed in a given circle of radius R.

$\displaystyle max\{S_{ABC}\}=max\{\frac{abc}{4R}\} $

$\displaystyle max\{S_{ABC}\}=max\{\frac{a^3}{4R},\frac{b^3}{4R}, \frac{c^3}{4R}$ hence, [tex}a=b=c[/tex]. - Jun 12th 2011, 06:49 AMayushdadhwal
let s=a+b+c where a,b,c are positive numbers .how can we prove that there sum is max. when they are equal.

- Jun 12th 2011, 06:50 AMayushdadhwal