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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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].