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Consider the following statements: Statement 1: The greatest possible number of intersection points formed by 8 circles of the same radius is 56. Statement 2: The greatest possible number of points of intersection obtained when 4 circles of different radii and 4 distinct straight lines are drawn is 50.

1. Statement 1 is correct, Statement 2 is correct, and Statement 2 correctly explains Statement 1
2. Statement 1 is correct, Statement 2 is correct, but Statement 2 does not correctly explain Statement 1
3. Statement 1 is incorrect, Statement 2 is correct
4. Statement 1 is correct, Statement 2 is incorrect

Correct answer: Statement 1 is correct, Statement 2 is correct, but Statement 2 does not correctly explain Statement 1

Solution

8 equal circles: each pair meets in at most 2 points, giving 2*C(8,2) = 56, so Statement 1 is correct. For 4 circles + 4 lines: circle-circle 2*C(4,2)=12, line-line C(4,2)=6, line-circle 4*4*2=32, total = 50, so Statement 2 is also correct, but it does not explain Statement 1.

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