Problem B. 4670. (December 2014)
B. 4670. Let \(\displaystyle A_1\), \(\displaystyle B_1\) and \(\displaystyle C_1\) be the midpoints of the sides of a triangle \(\displaystyle ABC\). Drop a perpendicular from \(\displaystyle A_1\) to the angle bisector drawn from vertex \(\displaystyle A\), from \(\displaystyle B_1\) to the angle bisector drawn from vertex \(\displaystyle B\), and from \(\displaystyle C_1\) to the angle bisector drawn from vertex \(\displaystyle C\). Let \(\displaystyle A_2\) denote the intersection of the perpendiculars from \(\displaystyle B_1\) and from \(\displaystyle C_1\). The points \(\displaystyle B_2\) and \(\displaystyle C_2\) are obtained in a similar way. Show that the lines \(\displaystyle A_1A_2\), \(\displaystyle B_1B_2\) and \(\displaystyle C_1C_2\) are concurrent.
Suggested by Zs. Sárosdi, Veresegyház
(3 pont)
Deadline expired on January 12, 2015.
Statistics:
36 students sent a solution.  
3 points:  Csépai András, Gál Boglárka, Geng Máté, GyulaiNagy Szuzina, Heinc Emília, Juhász 326 Dániel, Kerekes Anna, Khayouti Sára, Nagy Dávid Paszkál, Németh 123 Balázs, Polgár Márton, Vankó Miléna, Várkonyi Dorka, Williams Kada. 
2 points:  Andó Angelika, Ratkovics Gábor, Sal Kristóf, Szakály Marcell, Szász Dániel Soma. 
1 point:  8 students. 
0 point:  9 students. 
