SOLUTION: Show that of all the rectangles inscribed in a circle of fixed radius, the square has the largest area.

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Question 803796: Show that of all the rectangles inscribed in a circle of fixed radius, the square has the largest area.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
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%28+r%5E2+%2B+r%5E2+%29=+sqrt%282+r%5E2%29

MAXIMUM area is: A+=sqrt%282+r%5E2%29%2Asqrt%282+r%5E2%29=%28+sqrt%282+r%5E2%29%29%5E2+=2+r%5E2