Multiple choice

If a triangle of maximum area is inscribed within a circle of radius $R$, then

$S=2{ R }^{ 2 }$
$\cfrac { 1 }{ { r }_{ 1 } } +\cfrac { 1 }{ { r }_{ 2 } } +\cfrac { 1 }{ { r }_{ 3 } } =\cfrac { \sqrt { 2 } +1 }{ R } $
$r=\left( \sqrt { 2 } -1 \right) R$
$s=\left( 1+\sqrt { 2 } \right) .2R$

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