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# Is the circumference of the circle with center O greater than 2(AB + C

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Math Expert
Joined: 02 Sep 2009
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Is the circumference of the circle with center O greater than 2(AB + C  [#permalink]

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14 Mar 2018, 02:34
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Difficulty:

45% (medium)

Question Stats:

76% (02:17) correct 24% (01:32) wrong based on 84 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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2018-03-14_1330.png [ 13.18 KiB | Viewed 901 times ]

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Re: Is the circumference of the circle with center O greater than 2(AB + C  [#permalink]

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14 Mar 2018, 02:35
Bunuel wrote:

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

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

Attachment:
2018-03-14_1330.png

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Re: Is the circumference of the circle with center O greater than 2(AB + C  [#permalink]

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14 Mar 2018, 04:15
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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Re: Is the circumference of the circle with center O greater than 2(AB + C  [#permalink]

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25 Mar 2018, 09:12

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.

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Re: Is the circumference of the circle with center O greater than 2(AB + C   [#permalink] 25 Mar 2018, 09:12
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