Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem K. 421. (September 2014)

K. 421. Point $\displaystyle A$ lies on a diameter in a circle of radius 30 units. The chord drawn through $\displaystyle A$, perpendicular to the diameter has a length of 18 units. How many chords does the circle have, other than the diameter, that pass through $\displaystyle A$ and have integer lengths?

(6 pont)

Deadline expired on October 10, 2014.

Statistics:

 95 students sent a solution. 6 points: Ágoston Tamás, Balázs Bence, Czémán Bálint, Czémán Dávid, Dévényi Dalma, Farkas Lilla, Gémesi Szabolcs, Harsányi Benedek, Járomi Bence, Kollár Johanna, Kovács András, Kubovics Márton, Kulcsár Simon, Mamuzsics Gergő Bence, Márton Anna, Mészáros Melinda, Nagy Viktor, Németh Csilla Márta, Németh Gergő, Németh Martin Tamás, Öcsi Rebeka, Péri Gergő Gábor, Rittgasszer Ákos, Sebestyén Ádám, Sisák László Sándor, Slenker Balázs, Szalay Gergő, Takács Nóra, Thuróczy Mylan, Tószegi Fanni, Walter Anna, Wenhardt Kata. 5 points: 35 students. 4 points: 9 students. 3 points: 2 students. 2 points: 4 students. 1 point: 3 students. 0 point: 7 students. Unfair, not evaluated: 3 solutions.

Problems in Mathematics of KöMaL, September 2014