#1
I am in trig now, so my teacher doesn't remember geometry. A few weeks ago i remembered how to prove that any quadrilateral inscribed in a circle with right angles (in other words a rectangle in a circle) has to be a square. If anyone has links or can briefly explain this again much help

i know this post may not make sense but thanks to all who try and help
#3
Any quadrilateral with right angles has to be square, if all the angles are right that is.


......or at least a rectangle.
Last edited by Powerhouse at Jan 15, 2009,
#4
The corners of the quad. intersect the circle and the distance from center point to corner is a radius. That being said the only way for a quad to have the measures be the same and lie within the circle is for it to be a square.
#5
That's not true though, its easily possible to inscribe a quadlilateral into a square with right angles but unequal sides
#6
Quote by Powerhouse
Any quadrilateral with right angles has to be square, if all the angles are right that is.


What about rectangles?
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#8
i remember it had to do with the fact that the radius makes something else equal so that it has to be a square.


Off to find my old geo book.
#9
Trust me, I tutor math at the calculus level at Purdue, its not true. It is possible to put a rectangle inside a circle and for it not to be a square.
Edit:
I do remember an optimization problem very similiar to this that I worked on where I proved that a square is the quadlilateral where all the corners lie on a circle that has the greatest area.
Last edited by Rabada at Jan 15, 2009,
#10
use the radius to bisect one of the 90 degree angles. double th radius and you now have the diameter of the circle. use the diameter to bisect opposite angles and calculate the hypotenuse of 2 right triangles. do the same thing to the other two right angles and now you ahve have two sides and need to find the hypotenuse. a^2+b^2=c^2 if you get the same answer for c then it's a square

I think that's right?
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Last edited by fallingforever at Jan 15, 2009,
#11
Quote by Rabada
Trust me, I tutor math at the calculus level at Purdue, its not true. It is possible to put a rectangle inside a circle and for it not to be a square.


This.

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Last edited by Axeman99 at Jan 15, 2009,
#12
Quote by Rabada
Trust me, I tutor math at the calculus level at Purdue, its not true. It is possible to put a rectangle inside a circle and for it not to be a square.


he's right you can definitely have a rectangle in a circle.
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#13
Quote by Axeman99
This.

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I do know that if you want to maximize the area of that rectangle, you will have to make it a square, but you need to use calculus to do that, so I don't think that is what you are thinking of