Mathematical and Physical Journal
for High Schools
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Problem B. 4657. (October 2014)

B. 4657. The radius of the inscribed circle of a triangle is \(\displaystyle r\), and the radius of the circumscribed circle is \(\displaystyle R\). Assume that \(\displaystyle R < r \big(\sqrt{2}+1\big)\). Does this condition imply that the triangle is acute-angled?

Suggested by T. Káspári, Paks

(5 pont)

Deadline expired on November 10, 2014.


Statistics:

71 students sent a solution.
5 points:Andi Gabriel Brojbeanu, Baran Zsuzsanna, Bodolai Előd, Coulibaly Patrik, Cseh Kristóf, Csépai András, Czirkos Angéla, Döbröntei Dávid Bence, Dömsödi Bálint, Fekete Panna, Geng Máté, Gergely Bence, Kátay Tamás, Katona Dániel, Kavas Katalin, Kerekes Anna, Kocsis Júlia, Kovács 246 Benedek, Kovács 972 Márton, Lengyel Ádám, Nagy Viktor, Nagy-György Pál, Nagy-György Zoltán, Németh 123 Balázs, Papp 893 Marcell, Pohli Anna, Porupsánszki István, Sal Kristóf, Schrettner Bálint, Schwarcz Tamás, Szebellédi Márton, Széles Katalin, Szőke Tamás, Telek Máté László, Tóth 111 Máté , Török Tímea, Török Zsombor Áron, Vankó Miléna, Williams Kada.
4 points:12 students.
3 points:10 students.
2 points:3 students.
1 point:1 student.
0 point:6 students.

Problems in Mathematics of KöMaL, October 2014