Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
 Already signed up? New to KöMaL?

# 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