If there are two circles of radius 6 each and a sphere has a radius of 10, how many points can the two circles intersect when put around the surface of the sphere?
I. 0
II. 1
III. 2
A) I only
B) III only
C) I and II only
D) II and III only
E) I, II and III
@kbj5332 where is this question from? It seems awkwardly worded to the point that even I’m not 100% confident on what the question is saying.
If both circles are contained on the surface of the sphere (similar to stretching a rubber band around a ball), then it’s possible to draw them in such a way that they intersect at 0, 1, or 2 points.
But it is a fun question to think about.
Picture a beach ball and two rings that are smaller than the ball. You can put the rings around the ball so that they don’t intersect at all just by arranging them parallel to the “equator” of the ball. (I’m picturing the Earth and the tropic lines.)
Then, tilt the two rings so that they just meet at the equator. That gives you one intersection point. Tilt them a little more and you get two intersection points.
This question was from the December SAT for internationals.
@MITer94 its from the december international / november usa test. Its not phrased perfectly but I hope you get the idea!
@kbj5332 yeah, the phrase “put around” caught me off guard - it just sounds awkward as a mathematics student, and there are better ways of phrasing it. Otherwise, not a bad question.
I mean we repeatedly said that the answer was 0, 1, and 2 on both the Nov. US SAT thread and the Dec. Int SAT thread.