nice little problem:

prove that for a given circle, the rectangle of greatest area, drawn within the circle such that each vertex lies on the circumference, is a square.

Question

nice little problem:

prove that for a given circle, the rectangle of greatest area, drawn within the circle such that each vertex lies on the circumference, is a square.

anonymous · Answer

have i written the problem clearly?

anonymous · Answer

A rectangle of the greatest area inscribed in a circle is a square ... Calculus allowed ?

anonymous · Answer

yes :) although i would be very interested in a non calc answer, as my solution was a calc one

experimentx · Answer

A(x) = 4*x * sqrt(r^2 - x^2)
maximizing this function will give your calc sol

anonymous · Answer

http://www.algebra.com/algebra/homework/Rectangles/Rectangles.faq.question.471487.html

anonymous · Answer

with geometry and trigonometry

experimentx · Answer

although ... i would like to hear the other non calc solution.

anonymous · Answer

Another function that can be used 4*cosX*sinX = Area

anonymous · Answer

my solution was the same as @m_charron2 's

anonymous · Answer

all valid solutions though and an interesting non calc one

anonymous · Answer

did you see the last one on the link I posted ? Simple and clear .

anonymous · Answer

yes very nice

experimentx · Answer

it seems that my way and 4*cosX*sinX = Area are equivalent.