Problem B. 4674. (December 2014)

B. 4674. On the circumscribed circle of triangle \(\displaystyle ABC\), a point \(\displaystyle X\) is moving along the arc \(\displaystyle AC\) not containing vertex \(\displaystyle B\). Let \(\displaystyle Y\) and \(\displaystyle Z\) denote the points on the extensions of side \(\displaystyle BA\) beyond \(\displaystyle A\) and side \(\displaystyle BC\) beyond \(\displaystyle C\), respectively, for which \(\displaystyle AY=AX\) and \(\displaystyle CZ=CX\). What is the locus of the midpoint of line segment \(\displaystyle YZ\)?

Suggested by E. Pozsonyi, Budapest

(5 pont)

Deadline expired on January 12, 2015.

Statistics:

40 students sent a solution.
5 points:	Baran Zsuzsanna, Cseh Kristóf, Csépai András, Döbröntei Dávid Bence, Fekete Panna, Gáspár Attila, Katona Dániel, Kerekes Anna, Kocsis Júlia, Kovács 972 Márton, Kovács Péter Tamás, Nagy-György Pál, Porupsánszki István, Schrettner Bálint, Schwarcz Tamás, Szebellédi Márton, Tóth Viktor, Vághy Mihály, Varga-Umbrich Eszter, Wei Cong Wu, Williams Kada.
4 points:	Lajkó Kálmán, Leitereg Miklós, Németh 123 Balázs, Szakács Lili Kata.
3 points:	7 students.
2 points:	2 students.
1 point:	3 students.
0 point:	3 students.

Problems in Mathematics of KöMaL, December 2014