Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# 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:

 128 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: 70 students. 2 points: 12 students. 1 point: 23 students. 0 point: 6 students.

Problems in Mathematics of KöMaL, December 2015