1. ## maximum area

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

Math Forum - Ask Dr. Math

3. Originally Posted by FernandoRevilla

Math Forum - Ask Dr. Math
Can someone check this(?):

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

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

$max\{S_{ABC}\}=max\{\frac{a^3}{4R},\frac{b^3}{4R}, \frac{c^3}{4R}$ hence, [tex}a=b=c[/tex].

4. 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.