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.
ParallelogramCircle.jpg [ 16.3 KiB | Viewed 983 times ]
PhD in Applied Mathematics
Love GMAT Quant questions and running.