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
Geometry - parallelograms and circles
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- Rahul@gurome
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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.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
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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Hi there!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
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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