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