Mathematical and Physical Journal
for High Schools
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# Problem C. 1302. (September 2015)

C. 1302. The tangents drawn from an exterior point $\displaystyle P$ to a given circle of radius $\displaystyle r$ and centre $\displaystyle O$ touch the circle at $\displaystyle Q$ and $\displaystyle R$. What should be the distance $\displaystyle |OP|$ so that the area of quadrilateral $\displaystyle PQOR$ is equal to the area of the circle?

(5 pont)

Deadline expired on October 12, 2015.

### Statistics:

 212 students sent a solution. 5 points: Bárány Tamás, Beke-Szabó Csenge, Busa 423 Máté, Csilling Eszter, Csuha Boglárka, Dávid Levente, Demeter Gergő, Édes Lili, Erdélyi Zsófia , Farkas 333 Dorottya, Fekete Ákos, Galambos Ágnes, Garamvölgyi István Attila, Geretovszky Anna, Grácin Ibolya, Heller-Szabó Anna, Hidy Gábor, Kamenár Gyöngyvér, Kaposi Benedek, Kassai Levente, Kis 999 Alexandra, Körmöczi Kitti , Magyar 257 Boglárka, Maksa Gergő, Mályusz Attila, Marozsák Tóbiás , Molnár 410 István, Páhoki Tamás, Pap-Takács Noémi, Paulovics Péter, Pinke Andrea, Póta Balázs, Sántha 001 Balázs, Sebe Anna, Simon Dóra, Slenker Balázs, Somogyi Márk, Szajbély Sámuel, Szécsi Adél Lilla, Szentistványi István János, Szögi Tamás, Tóth 111 Máté , Tóth 953 Eszter, Török 111 Emese, Tubak Dániel, Uzonyi 000 Ákos, Varga 274 Tamás, Veres Károly, Weisz Máté, Zsombó István. 4 points: 56 students. 3 points: 44 students. 2 points: 33 students. 1 point: 24 students. 0 point: 4 students. Unfair, not evaluated: 1 solution.

Problems in Mathematics of KöMaL, September 2015