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