Problem A. 786. (November 2020)

A. 786. In a convex set \(\displaystyle S\) that contains the origin it is possible to draw \(\displaystyle n\) disjoint unit circles such that viewing from the origin non of the unit circles blocks out a part of another (or a complete) unit circle. Prove that the area of \(\displaystyle S\) is at least \(\displaystyle n^2/100\).

Submitted by: Dömötör Pálvölgyi, Budapest

(7 pont)

Deadline expired on December 10, 2020.

Statistics:

11 students sent a solution.
7 points:	Bán-Szabó Áron, Fleiner Zsigmond, Füredi Erik Benjámin, Hegedűs Dániel, Kovács 129 Tamás, Molnár-Szabó Vilmos, Seres-Szabó Márton, Sztranyák Gabriella, Várkonyi Zsombor.
4 points:	1 student.
1 point:	1 student.

Problems in Mathematics of KöMaL, November 2020