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A Point Set and Seven Circles

Source: 1986 National High School Mathematics League, Exam One, Problem 5

February 24, 2020

Problem Statement

There is a point set on a plane, and seven circles C1,C2,⋯ ,C7C_1,C_2,\cdots,C_7, where C7C_7 passes exactly 7 points in MM, C6C_6 passes exactly 6 points in MM, ..., C1C_1 passes exactly 1 point in MM. Then how many points do set MM have at least? (A)11(B)12(C)21(D)28\text{(A)}11\qquad\text{(B)}12\qquad\text{(C)}21\qquad\text{(D)}28
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