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555-605 (Medium)|   Geometry|      
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Is the circumference of the circle with center O greater than 2(AB + C 14 Mar 2018, 02:34
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A
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74% (02:18) correct 26% (01:54) wrong based on 182 sessions

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Is the circumference of the circle with center O greater than 2(AB + CD) ?

(1) CD = AB/2
(2) x = 90

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Is the circumference of the circle with center O greater than 2(AB + C 14 Mar 2018, 02:35
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Is the circumference of the circle with center O greater than 2(AB + CD) ?

(1) CD = AB/2
(2) x = 90

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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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Is the circumference of the circle with center O greater than 2(AB + C 14 Mar 2018, 04:15
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Answer is A.
Let us take r= radius of circle.
AB=2 r
Circumference of circle = 2*pi*r
Statement 1: CD=AB/2.
CD=r
2(AB+CD) =2( 2r + r) =6r.
Circumference of circle = 6.28r
6.28r is greater than 6 r.
Statement 1 is sufficient.

Statement 2. x = 90 degree
Max value of CD can be 2r.
Min value of CD will tend to 0.
2(AB+CD) will range from 8 r to 4 r. 6.28 r will lie in between 8 r and 4 r.
So it is not sufficient.


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Is the circumference of the circle with center O greater than 2(AB + C 25 Mar 2018, 09:12
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Solution



We need to find whether circumference of the circle is more than 2(AB+CD) or not.

    •The circumference of the circle= \(2*π *r =2* 3.14*r\), where r is the radius of the circle.
    • Since AB passes through the centre of the circle, AB is the diameter of the circle.
      o AB=2r
      o 2(AB+CD) = 2(2r+CD)
         2(2r+CD) is greater than \(2*3.14*r\) if CD is greater than \(1.14r\).

Thus, If \(CD> 1.14r\), then:
    • Yes, the circumference of the circle with center O is greater than 2(AB + CD).
    • No, the circumference of the circle with center O is NOT greater than 2(AB + CD)

Statement-1 “\(CD = \frac{AB}{2}\)”.

AB passes through the centre of the circle. Hence, AB is the diameter of the circle.

    • \(AB= 2r\)
    • \(CD=r\)
      o \(r< 1.14r\)

Hence, Statement 1 alone is sufficient to answer the question.

Statement-2 “\(x = 90\)”.



Since the value of angle \(x\) does not give us information about the length of CD, Statement 2 alone is not sufficient to answer the question.


Answer: A
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Is the circumference of the circle with center O greater than 2(AB + C 06 Dec 2022, 14:28
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Solution



We need to find whether circumference of the circle is more than 2(AB+CD) or not.

    •The circumference of the circle= \(2*π *r =2* 3.14*r\), where r is the radius of the circle.
    • Since AB passes through the centre of the circle, AB is the diameter of the circle.
      o AB=2r
      o 2(AB+CD) = 2(2r+CD)
         2(2r+CD) is greater than \(2*3.14*r\) if CD is greater than \(1.14r\).

Thus, If \(CD> 1.14r\), then:
    • Yes, the circumference of the circle with center O is greater than 2(AB + CD).
    • No, the circumference of the circle with center O is NOT greater than 2(AB + CD)

Statement-1 “\(CD = \frac{AB}{2}\)”.

AB passes through the centre of the circle. Hence, AB is the diameter of the circle.

    • \(AB= 2r\)
    • \(CD=r\)
      o \(r< 1.14r\)

Hence, Statement 1 alone is sufficient to answer the question.

Statement-2 “\(x = 90\)”.



Since the value of angle \(x\) does not give us information about the length of CD, Statement 2 alone is not sufficient to answer the question.


Answer: A
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I understand that the figure is not drawn to scale. But we can see that line CD connects two points on a circle and doesn't pass the center. Doesn't that mean that CD is always a non-diameter chord, hence takes values from 0 < CD < 2 and is always smaller than the diameter (AB)?
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