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23 May 2022, 01:30
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Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
(A) 8
(B) 9
(C) 10
(D) 12
(E) 16
Are You Up For the Challenge: 700 Level Questions
(A) 8
(B) 9
(C) 10
(D) 12
(E) 16
Are You Up For the Challenge: 700 Level Questions
23 May 2022, 06:20
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Drawing out two circles intersecting, one notices that the most two circles can intersect is twice. Let each circle be represented by numbers 1 through to 4.
1 and 2 will intersect twice. Now let 3 be bigger and let it intersect both twice (four intersections in total). Now let 4 be the biggest circle, and it too will intersect 1,2&3 twice each(6 in total). That means that in total there are a total of: \(2+4+6 = 12\) intersections that occur between all four circles.
Answer D
1 and 2 will intersect twice. Now let 3 be bigger and let it intersect both twice (four intersections in total). Now let 4 be the biggest circle, and it too will intersect 1,2&3 twice each(6 in total). That means that in total there are a total of: \(2+4+6 = 12\) intersections that occur between all four circles.
Answer D
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