Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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# Problem K. 429. (October 2014)

K. 429. The measure of the angle lying at vertex $\displaystyle C$ of an isosceles triangle $\displaystyle ABC$ is $\displaystyle 120^\circ$. The perpendicular bisectors of the legs intersect the base at the points $\displaystyle D$ and $\displaystyle E$. Show that the area of triangle $\displaystyle ABC$ is three times the area of triangle $\displaystyle CDE$.

(6 pont)

Deadline expired on November 10, 2014.

### Statistics:

 110 students sent a solution. 6 points: Béda Gergely, Csilling Eszter, Csuha Boglárka, Dévényi Dalma, Farkas Lilla, Farkas Panka, Fekete Balázs Attila, Harsányi Benedek, János Zsuzsa Anna, Járomi Bence, Kollár Johanna, Kós Anna, Kovács 124 Marcell, Kovács Marcell Dorián , Kulcsár Simon, Majzik Bendegúz Dániel, Mészáros Melinda, Mihályházi Péter, Németh 962 Ambrus, Németh Csilla Márta, Németh Levente , Oravecz Janka Éva, Orova Katinka, Öcsi Rebeka, Paulovics Péter, Rimai 217 Dániel, Sipos Fanni Emma, Sisák László Sándor, Slenker Balázs, Szalay Csilla, Szalay Gergő, Szarka Álmos, Tamási Kristóf Áron, Thuróczy Mylan, Tószegi Fanni, Valkó Bence, Varga 274 Tamás. 5 points: 26 students. 4 points: 9 students. 3 points: 10 students. 2 points: 13 students. 1 point: 7 students. 0 point: 3 students. Unfair, not evaluated: 5 solutions.

Problems in Mathematics of KöMaL, October 2014