Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem A. 693. (March 2017)

A. 693. Let \(\displaystyle A\) and \(\displaystyle B\) be two vertices of a convex polygon \(\displaystyle \mathcal{P}\) with maximum distance from each other. Let the perpendicular bisector of the segment \(\displaystyle AB\) meet the boundary of \(\displaystyle \mathcal{P}\) at points \(\displaystyle C\) and \(\displaystyle D\). Show that the perimeter of \(\displaystyle \mathcal{P}\) is less than \(\displaystyle 2(AB+CD)\).

(5 pont)

Deadline expired on April 10, 2017.


Statistics:

8 students sent a solution.
5 points:Baran Zsuzsanna, Bukva Balázs, Gáspár Attila, Imolay András, Matolcsi Dávid, Williams Kada.
1 point:2 students.

Problems in Mathematics of KöMaL, March 2017