The triangle of maximum area that can be inscribed in a given circle of radius ‘r’ is 

$\text{ An equilateral triangle of height }\frac{2r}{3}$

$\text{ An isosceles triangle with base equal to }2r$

A right angle triangle having two of its sides of length 2r and r

$\text{ An equilateral triangle having each of its side of length }\sqrt{3}r$