Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 460. (March 2015)

K. 460. A circle of radius 10 units is centred at point $\displaystyle O$. $\displaystyle A$, $\displaystyle B$ and $\displaystyle C$ are points on the circle such that $\displaystyle O$ lies in the interior of triangle $\displaystyle ABC$. Given that the length of line segment $\displaystyle AB$ is 12 units and the measure of angle $\displaystyle ABC$ is $\displaystyle 60^\circ$, find

$\displaystyle a)$ the distance of point $\displaystyle O$ from line segment $\displaystyle AB$,

$\displaystyle b)$ the length of line segment $\displaystyle AC$.

(6 pont)

Deadline expired on April 10, 2015.

### Statistics:

 60 students sent a solution. 6 points: Agócs Katinka, Ágoston Tamás, Benda Orsolya, Csilling Eszter, Csuha Boglárka, Dévény Csaba, Encz Koppány, Farkas Lilla, Fekete Balázs Attila, Filip Krisztina, Harsányi Benedek, János Zsuzsa Anna, Lakatos Ágnes, Maksa Gergő, Márton Anna, Mészáros Melinda, Nagy Marcell, Németh Csilla Márta, Paulovics Péter, Péri Gergő Gábor, Pintér 345 Balázs, Posch Levente Ágoston, Rátkai Petra, Sipos Fanni Emma, Sisák László Sándor, Slenker Balázs, Szakali Benedek, Szalay Gergő, Szarka Álmos, Szűcs 865 Eszter, Tamási Kristóf Áron, Tószegi Fanni, Valkó Bence, Varga 274 Tamás, Wenczel Kata. 5 points: Bakó Csenge, Farkas Panka, Kóczán Kristóf, Kollár Johanna, Sziráki Boglárka Tünde. 4 points: 2 students. 3 points: 2 students. 2 points: 11 students. 1 point: 2 students. 0 point: 1 student. Unfair, not evaluated: 2 solutionss.

Problems in Mathematics of KöMaL, March 2015