2002 IMO Problems/Problem 6

Revision as of 00:38, 19 November 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>n \ge 3</math> be a positive integer. Let <math>C_1,C_2,...,C_n</math> be unit circles in the plane, with centers <math>O_1,O_2,...,O_n</math> respecti...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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

This problem needs a solution. If you have a solution for it, please help us out by adding it.

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