2002 IMO Problems/Problem 6

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Problem

Let $n \ge 3$ be a positive integer. Let $C_1,C_2,...,C_n$ be unit circles in the plane, with centers $O_1,O_2,...,O_n$ respectively. If no line meets more than two of the circles, prove that

\[\sum_{1\le i< j \le n}^{}\frac{1}{O_iO_j}\le\frac{(n-1)\pi}{4}\]

Solution

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See Also

2002 IMO (Problems) • Resources
Preceded by
Problem 5
1 2 3 4 5 6 Followed by
Last Problem
All IMO Problems and Solutions