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605-655 (Medium)|   Geometry|      
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asmit123
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Which of the following lists the number of points at which a circle ca 21 May 2011, 05:18
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E
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45% (medium)

Question Stats:

54% (01:05) correct 46% (01:45) wrong based on 198 sessions

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Which of the following lists the number of points at which a circle can intersect a square ?

A. 2 & 8 only
B. 2, 4 & 8 only
C. 2, 4, 6 & 8 only
D. 1, 2, 3, 4, 6 & 8 only
E. 1, 2, 3, 4, 5, 6, 7 & 8 only
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E
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hussi9
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Which of the following lists the number of points at which a circle ca 21 May 2011, 05:35
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Not sure if I am correct.

But seems to be quite right
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Circle.JPG [ 18.14 KiB | Viewed 10987 times ]

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Bunuel
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Which of the following lists the number of points at which a circle ca 27 Jan 2022, 04:42
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asmit123
Which of the following lists the number of points at which a circle can intersect a square ?

A. 2 & 8 only
B. 2, 4 & 8 only
C. 2, 4, 6 & 8 only
D. 1, 2, 3, 4, 6 & 8 only
E. 1, 2, 3, 4, 5, 6, 7 & 8 only
Show more

Similar questions:
https://gmatclub.com/forum/which-of-the ... 92274.html (triangle)
https://gmatclub.com/forum/which-of-the ... 38952.html (parallelogram)
https://gmatclub.com/forum/which-of-the ... 14013.html (square)
https://gmatclub.com/forum/what-is-the- ... 97855.html (10 circles)
https://gmatclub.com/forum/gmatbusters- ... 16475.html (6 circles)
https://gmatclub.com/forum/what-is-the- ... 10362.html (11 circles)
https://gmatclub.com/forum/which-of-the ... 80597.html (two parallel lines)

Hope it helps.
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asmit123
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Which of the following lists the number of points at which a circle ca 21 May 2011, 07:56
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oh..i did not expect tangent to be called as intersection ...
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hussi9
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Which of the following lists the number of points at which a circle ca 21 May 2011, 07:58
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asmit123
oh..i did not expect tangent to be called as intersection ...
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Tangent intersects the circle at exactly one point :P

Anyways this question is hard to get at first time... Unless you have good imagination skills... I dont thin any formula can help

Now that we know it should be simple
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GMATSkilled
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Which of the following lists the number of points at which a circle ca 16 Jun 2018, 21:11
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asmit123
Which of the following lists the no. of points at which a circle can intersect a square ?

A. 2 & 8 only
B. 2, 4 & 8 only
C. 2, 4, 6 & 8 only
D. 1, 2, 3, 4, 6 & 8 only
E. 1, 2, 3, 4, 5, 6, 7 & 8 only
Show more

EvaJager has solved this here: https://gmatclub.com/forum/which-of-the ... l#p1121790
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GyMrAT
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Which of the following lists the number of points at which a circle ca 17 Jun 2018, 00:52
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asmit123
Which of the following lists the no. of points at which a circle can intersect a square ?

A. 2 & 8 only
B. 2, 4 & 8 only
C. 2, 4, 6 & 8 only
D. 1, 2, 3, 4, 6 & 8 only
E. 1, 2, 3, 4, 5, 6, 7 & 8 only
Show more

Had to use some Sc-fi imagination for this question :-D

Think of a moving circle which can vary in size & a fixed square of constant dimensions. Now imagine the circle eclipsing the square kinda like the shadow of moon eclipsing the Sun, if you have seen images or videos of a Solar eclipse or if you are a fan of Sci fi movies like me, it will be easy to imagine. Makes me wanna watch Interstellar for the nth time.

Well back to question.

Now the moving circle is inching towards the square from outside, first touching the square at one of its corner. That is our Point 1 of intersection. Hence we are down to options D & E.

Now the circle keeps moving forward gobbling the square, intersecting two sides & still moving forward. There will come a point when the circle can touch one side tangentially & intersect two other sides each at two points. That is 5 points of intersection . Only answer choice E has 5.

Hence Answer is E.

Thanks,
GyM

Ps. You can insert Hans Zimmer's back ground score from Interstellar for added effect while moving the circle, certainly helped me.
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Which of the following lists the number of points at which a circle ca 29 Jun 2022, 23:39
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do we have a formula to solve this instead of actually plotting the points?
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Which of the following lists the number of points at which a circle ca 05 Nov 2024, 15:37
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