Problem C. 1323. (December 2015)

C. 1323. Let \(\displaystyle T\) denote the intersection of side \(\displaystyle BC\) with the angle bisector drawn from vertex \(\displaystyle A\) of a right-angled triangle. Let \(\displaystyle F\) denote the midpoint of side \(\displaystyle BC\), and let \(\displaystyle M\) be the intersection of the perpendicular bisector drawn at \(\displaystyle F\) with another side. Given that the quadrilateral \(\displaystyle ATFM\) is a kite, determine the angles of the triangle. (\(\displaystyle A\) may denote any vertex of the triangle.)

(5 pont)

Deadline expired on January 11, 2016.

Statistics:

127 students sent a solution.
5 points:	Dávid Levente, Édes Lili, Fekete Balázs Attila, Fraknói Ádám, Jánosdeák Márk, Marozsák Tóbiás , Páhoki Tamás, Weisz Máté.
4 points:	Balogh 999 Árpád Mátyás, Fazekas 15 Levente, Malák Péter, Máth Benedek, Pinke Andrea, Szilágyi Éva, Tóth 111 Máté , Tubak Dániel, Veres Bálint.
3 points:	69 students.
2 points:	12 students.
1 point:	23 students.
0 point:	6 students.

Problems in Mathematics of KöMaL, December 2015