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Geometry - parallelograms and circles

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by koby_gen » Fri Jan 21, 2011 1:30 am
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
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by Rahul@gurome » Fri Jan 21, 2011 1:51 am
koby_gen 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
Note that if a line just touches a circle, i.e. the line is a tangent to the circle, then it is considered that the line intersects the circle at one point. Thus a line can intersect a circle at either 1 or 2 points.

A parallelogram has 4 lines.
Hence, it can intersect a circle at either 1, 2, 3, 4, 5, 6, 7, or 8 points.

The correct answer is E.
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by fskilnik@GMATH » Fri Jan 21, 2011 1:54 am
koby_gen 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
Hi there!

Let us admit the problem is well-stated (as usually is), therefore from my first drawing we know the answer must be (C) or (E). From my second drawing, we are sure the answer is [spoiler] (E) [/spoiler].

Regards,
Fábio.

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