Mathematical and Physical Journal
for High Schools
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# Problem C. 1271. (January 2015)

C. 1271. Consider circumscribed circle of a right-angled triangle. Draw the semicircle containing the triangle, and draw tangents to it, parallel to the legs. The parallels together with the line of the hypotenuse form a similar right-angled triangle.

Find the angles of the triangle if the area of the outer triangle is 6 times the area of the inner triangle.

Based on the idea of I. Légrádi, Sopron

(5 pont)

Deadline expired on February 10, 2015.

### Statistics:

 39 students sent a solution. 5 points: Bese Csongor, Bodonhelyi Anna, Bottlik Judit, Chourfi Abdel Karim, Egyházi Anna, Erdei Ákos, Fehér Balázs, Fülöp Erik, Horváth 016 Gábor, Kasó Ferenc, Kósa Szilárd, Krisztián Jonatán, Mándoki Sára, Matusek Márton, Mátyus Adrienn, Pap-Takács Mónika, Sándor Gergely, Sudár Ákos, Szabó 157 Dániel, Szűcs Dorina, Szücs Patrícia, Varjas István Péter, Vida Máté Gergely. 4 points: Farkas Dóra, Lénárt Levente, Mészáros 01 Viktória, Porupsánszki István, Sziegl Benedek, Telek Máté László. 3 points: 3 students. 2 points: 1 student. 1 point: 3 students. 0 point: 3 students.

Problems in Mathematics of KöMaL, January 2015