Prove that the rectangle with greatest area that can be inscribed in a circle is a square and find an expression for the length of the sides of this square.
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Last edited by Ano123; 10-09-2016 at 18:37.
- 10-09-2016 18:33
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(Original post by Ano123)
- 10-09-2016 18:35
Prove that the rectangle that can be inscribed in a circle with greatest area is a square and find an expression for the length of the sides of this square.
Start with a circle of radius and centre O. Inscribe a rectangle with lengths and .
The area of the rectangle is . Express a and b in terms of and from cosine rule if you let theta equal the angle between ON and OM where NM=a and ON=OM=r. Same idea for the b side.
Then once you have A in terms of r and theta, differentiate A with respect to theta and maximise it by making it equal to 0. You should find the angle which makes the area max, and apply it to a and b. You should find that a=b in terms of r therefore it's a square.Last edited by RDKGames; 10-09-2016 at 19:08.
- 10-09-2016 19:05