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# Which of the following lists the number of points at which a

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Which of the following lists the number of points at which a [#permalink]

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15 Sep 2012, 07:39
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Which of the following lists the number of points at which a circle can intersect a parallelogram?

(A) 2, 4, and 8 only
(B) 2, 4, 6, and 8 only
(C) 1, 2, 3, 4, 6, and 8 only
(D) 2, 3, 4, 5, 6, 7, and 8 only
(E) 1, 2, 3, 4, 5, 6, 7, and 8
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Sep 2012, 09:17, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Which of the following lists the number of points at which a [#permalink]

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15 Sep 2012, 09:41
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Viru wrote:
Which of the following lists the number of points at which a circle can intersect a parallelogram?

(A) 2, 4, and 8 only
(B) 2, 4, 6, and 8 only
(C) 1, 2, 3, 4, 6, and 8 only
(D) 2, 3, 4, 5, 6, 7, and 8 only
(E) 1, 2, 3, 4, 5, 6, 7, and 8

It is much easier to think of the intersection points between a square and a circle. Obviously, a square is a special parallelogram.

A square can intersect a circle in 8 points. See the attached drawing (leftmost figure).
There can be also 7 points of intersection, when one of the sides is tangent to the circle (middle figure). We are down to choose between D and E.
Finally, there can be only one point of intersection, when just one side is tangent to the circle (rightmost figure).
The only choice we are left with is E.

On a real test, you should not spend time to check all possible intersections.
Now, you can try to figure out all the options.
2 and 4 is easy. For 3, 5, and 6 intersection points, consider a rectangle.

Attachments

ParallelogramCircle.jpg [ 16.3 KiB | Viewed 3140 times ]

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Re: Which of the following lists the number of points at which a [#permalink]

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15 Sep 2012, 10:51
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Expert's post
Viru wrote:
Which of the following lists the number of points at which a circle can intersect a parallelogram?

(A) 2, 4, and 8 only
(B) 2, 4, 6, and 8 only
(C) 1, 2, 3, 4, 6, and 8 only
(D) 2, 3, 4, 5, 6, 7, and 8 only
(E) 1, 2, 3, 4, 5, 6, 7, and 8

Similar question to practice: which-of-the-following-lists-the-number-of-points-at-which-a-92274.html

Hope it helps.
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Re: Which of the following lists the number of points at which a [#permalink]

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15 Sep 2012, 22:51
Thanks for the explanation, EvaJager & Bunuel
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Re: Which of the following lists the number of points at which a [#permalink]

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25 Sep 2014, 11:15
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Re: Which of the following lists the number of points at which a   [#permalink] 25 Sep 2014, 11:15
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