The maximum area of the rectangle that can be inscribed in a circle of radius r is

Step-by-step solution

Refer figure aligned & B =( r , r ) & Ab 2 r and BC =2 r & Area ( ABCD )= AB BC & f ( )=(2 r )(2 r )=2 r ^2 2 & f ^ ( )=4 r ^2 2 and when f ^ ( )=0 , we write & 2 =0 2 = 2 = 4 & f ^ ( )=-8 r ^2 2 and f ^ ( )_ [ = 4 ] =-8 r ^2 < 0 aligned Thus, area of required rectangle is maximum when = 4 aligned & AB =2 r 4 =2 r ( 1 2 )= 2 r and & BC =2 r 4 =2 r ( 1 2 )= 2 r aligned Maximum Area ( ABCD )==( 2 r )( 2 r )=2 r ^2