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A rectangle is inscribed in a unit circle. Find the largest possible area of the rectangle.

 Mar 25, 2020
 #1
avatar+1970 
+1

Hint:

 

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

 

This is a diagram that represents this situation

 Mar 25, 2020
 #2
avatar+111330 
+1

The  lagest   possible rectangle will be  a  square with  a diagonal of 2

 

The side of this square  =   2/√2

 

So......the area of this square =  (2/√2)^2 =  4/2  =  2 units^2

 

 

cool cool cool

 Mar 25, 2020
 #3
avatar+1970 
+2

Awesome, Chris!

CalTheGreat  Mar 25, 2020

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