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Re M2405
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16 Sep 2014, 01:20
Official Solution: A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle? I. 0.01 II. 2.00 III. 3.20 A. I only B. II only C. III only D. I and II only E. II and III only Look at the diagram below: If the width of blue rectangle is small enough then its area could be 0.01. Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle). Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible) Answer: D
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Re M2405
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19 Mar 2015, 06:06
I think this question is good and helpful. Hi, could you please explain why the area of the inscribed square in a circle with the diameter of 2 is 2?



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19 Mar 2015, 06:13



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26 Sep 2016, 01:08
After reading this explanation, I came up with this doubt: If we draw the diagonals of the rectangle (the blue region), each of the diagonals would pass through the center which would be same as the diameter of the circle. Right or wrong? I am not able to prove this wrong.



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26 Sep 2016, 02:34



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Then should the area of the rectangle be 1/2*d1*d2= 1/2*2*2=2?. I think I am getting this wrong, but where I don't know.



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05 Apr 2017, 10:55
This is a great question. Very enlightening. There is a question about a small ''technicallity'' though.
The question stem asks about a ''rectangle''. Since the area of 2 is only achieved throught a square isn't it provoking a little doubt that you could marginally discard the area =2 because ''technically'' the questions asks about rectangle ?
I hope my question is not awkwardly written



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26 Oct 2017, 12:42
Bunuel wrote: Official Solution: A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle? I. 0.01 II. 2.00 III. 3.20 A. I only B. II only C. III only D. I and II only E. II and III only Look at the diagram below: If the width of blue rectangle is small enough then its area could be 0.01. Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle). Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible) Answer: D Hello Bunueli have a question for the highlighted area  shouldn't the max area of square inscribed within a circle with diameter of 2 be 2*pi? let a = side of square... diameter = diagonal 2 = a*sqrt(2) a = sqrt(2). Area = pi*a^2 = 2*pi. So => 0 <= area < 2*pi Please let me know if i am missing something!!!



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26 Oct 2017, 21:41
manishtank1988 wrote: Bunuel wrote: Official Solution: A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle? I. 0.01 II. 2.00 III. 3.20 A. I only B. II only C. III only D. I and II only E. II and III only Look at the diagram below: If the width of blue rectangle is small enough then its area could be 0.01. Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle). Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible) Answer: D Hello Bunueli have a question for the highlighted area  shouldn't the max area of square inscribed within a circle with diameter of 2 be 2*pi? let a = side of square... diameter = diagonal 2 = a*sqrt(2) a = sqrt(2). Area = pi*a^2 = 2*pi. So => 0 <= area < 2*pi Please let me know if i am missing something!!! Not sure what you are doing there. If a square is inscribed in a circle with the diameter of 2, then the area of the square would simply be diagonal^2/2 = 4/2 = 2 (because diameter=diagonal).
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Re: M2405
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27 Oct 2017, 09:14
Bunuel wrote: manishtank1988 wrote: Bunuel wrote: Official Solution: A rectangle is inscribed in a circle of diameter 2. Which of the following can be the area of the rectangle? I. 0.01 II. 2.00 III. 3.20 A. I only B. II only C. III only D. I and II only E. II and III only Look at the diagram below: If the width of blue rectangle is small enough then its area could be 0.01. Generally, the area of the inscribed rectangle is more than 0 and less than or equal to the area of the inscribed square (inscribed square has the largest area from all rectangles that can be inscribed in a given circle). Now, since the area of the inscribed square in a circle with the diameter of 2 is 2, then the area of the inscribed rectangle is \(0 \lt area \le 2\). So, I and II are possible values of the area. (Else you can notice that the area of the circle is \(\pi r^2=\pi \approx 3.14\) and the area of the inscribed rectangle cannot be greater than that, so III is not possible) Answer: D Hello Bunueli have a question for the highlighted area  shouldn't the max area of square inscribed within a circle with diameter of 2 be 2*pi? let a = side of square... diameter = diagonal 2 = a*sqrt(2) a = sqrt(2). Area = pi*a^2 = 2*pi. So => 0 <= area < 2*pi Please let me know if i am missing something!!! Not sure what you are doing there. If a square is inscribed in a circle with the diameter of 2, then the area of the square would simply be diagonal^2/2 = 4/2 = 2 (because diameter=diagonal). Hello BunuelI got my mistake  we are talking about largest rectangle (square) within a circle  thus area of square  a^2 => 2. My bad.



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12 Apr 2018, 07:32
+1 for option D. The key take away is that one shouldn't fail to consider boundary cases while evaluating options. Here if you overlook the fact that all squares are rectangle , you are bound to get it wrong !!! Great question
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23 Aug 2018, 00:20
Can we say that because the rectangle is inside the circle, the area of the rectangle must be <= that of circle. the area of the circle is 3.14, therefore the area of the rectangle must be <=3.14?



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23 Aug 2018, 00:28










