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

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

by AAPL » Sun Jan 20, 2019 6:26 am

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Which of the following lists a number of points at which a circle intersects a triangle?

A. 2 and 6 only
B. 2, 4 and 6 only
C. 1, 2, 3 and 6 only
D. 1, 2, 3, 4 and 6 only
E. 1, 2, 3, 4, 5 and 6 only

OA E
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by Brent@GMATPrepNow » Sun Jan 20, 2019 6:49 am
AAPL wrote:GMAT Prep

Which of the following lists a number of points at which a circle intersects a triangle?

A. 2 and 6 only
B. 2, 4 and 6 only
C. 1, 2, 3 and 6 only
D. 1, 2, 3, 4 and 6 only
E. 1, 2, 3, 4, 5 and 6 only

OA E
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Answer: E

The important takeaway here is that "intersect" does not necessarily mean "pass through"
So, a line that is tangent to a circle (touching the circle but not passing through it) can be said to intersect the circle. To intersect is to share a common point.

ALTERNATIVELY, if we can show that it's possible to have 5 points of intersection, then we can ELIMINATE answer choices A, B, C, and D, leaving us with answer choice E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Mon Jan 21, 2019 5:25 am
Brent@GMATPrepNow wrote: if we can show that it's possible to have 5 points of intersection, then we can ELIMINATE answer choices A, B, C, and D, leaving us with answer choice E
In the post above, Brent offers an explicit construction (i.e., a constructible figure) in which "5 points of intersection" is PROVED possible.

Once this explicit construction was done, we believe the argument above is not only rigorous, but faster. In other words, the best approach.

Regards,
Fabio.
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