Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem B. 4713. (April 2015)

B. 4713. A circle passing through vertices $\displaystyle B$ and $\displaystyle C$ of triangle $\displaystyle ABC$ intersects side $\displaystyle AB$ at $\displaystyle D$, and side $\displaystyle AC$ at $\displaystyle E$. The intersection of lines $\displaystyle CD$ and $\displaystyle BE$ is $\displaystyle O$. Let $\displaystyle M$ denote the centre of the inscribed circle of triangle $\displaystyle ADE$, and let $\displaystyle N$ denote the centre of the inscribed circle of triangle $\displaystyle ODE$. Prove that line $\displaystyle MN$ bisects the smaller arc $\displaystyle DE$.

(6 pont)

Deadline expired on May 11, 2015.

### Statistics:

 4 students sent a solution. 6 points: Csépai András. 5 points: Fekete Panna, Nagy-György Pál, Williams Kada.

Problems in Mathematics of KöMaL, April 2015