Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation

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Problem A. 397. (March 2006)

A. 397. Given n unit circle (n $\ge$ 3) in the plane, their centers are O₁,O₂,...,O_n. Any line of the plane intersects at most two of them. Show that

$\sum_{1\le i<j\le n}\frac1{O_iO_j}\le\frac{(n-1)\pi}4.$

(5 pont)

Deadline expired on April 18, 2006.

Statistics:

9 students sent a solution.

5 points: Erdélyi Márton, Estélyi István, Hujter Bálint, Nagy 224 Csaba, Paulin Roland.

4 points: Fischer Richárd, Kisfaludi-Bak Sándor, Sümegi Károly, Tomon István.

Problems in Mathematics of KöMaL, March 2006

9 students sent a solution.
5 points:	Erdélyi Márton, Estélyi István, Hujter Bálint, Nagy 224 Csaba, Paulin Roland.
4 points:	Fischer Richárd, Kisfaludi-Bak Sándor, Sümegi Károly, Tomon István.