Question 471487

NOTE: A rectangle INSCRIBED in a circle is ALWAYS a SQUARE IF you have to get MAXIMUM area.

 
let {{{A}}},{{{ B}}},{{{ C}}},and {{{D}}} be the vertices of the square 

the diagonals {{{AC}}} and diagonal {{{BD}}} will intersect at right angles so

the side of a square is {{{A= sqrt( r^2 + r^2 )= sqrt(2 r^2)}}}


MAXIMUM area is: {{{A =sqrt(2 r^2)*sqrt(2 r^2)=( sqrt(2 r^2))^2 =2 r^2}}}