Is sides of rectangle touch a circle prove that it is square?
Answers
Answered by
2
If L and W denote the length and width of a rectangle, and the radius of the circle is r, then
 (by the Pythagorean theorem)
Hence, we can say that , and that
 (A denotes the area of the rectangle)

By AM-GM inequality,


The left side is a constant, so we can say that the area is maximized in the equality case, which occurs if and only if

In other words, the area is maximized when the rectangle is a square.
 (by the Pythagorean theorem)
Hence, we can say that , and that
 (A denotes the area of the rectangle)

By AM-GM inequality,


The left side is a constant, so we can say that the area is maximized in the equality case, which occurs if and only if

In other words, the area is maximized when the rectangle is a square.
Similar questions