English Információ A lap Pontverseny Cikkek Hírek Fórum

Rendelje meg a KöMaL-t!

VersenyVizsga portál

Kísérletek.hu

Matematika oktatási portál

A. 507. The circles $\displaystyle K_1,\dots,K_6$ are externally tangent to the circle $\displaystyle K_0$ in this order. For each $\displaystyle 1\le i\le 5$, the circles $\displaystyle K_i$ and $\displaystyle K_{i+1}$ are externally tangent to each other, and $\displaystyle K_1$ and $\displaystyle K_6$ are externally tangent to each other as well, according to the Figure. Denote by $\displaystyle r_i$ the radius of $\displaystyle K_i$ ($\displaystyle 0\le i\le6$). Prove that if $\displaystyle r_1r_4=r_2r_5=r_3r_6=1$ then $\displaystyle {r_0\le 1}$.

Proposed by: Balázs Strenner, Székesfehérvár

(5 points)

Deadline expired on 10 May 2010.

Statistics on problem A. 507.
 2 students sent a solution. 4 points: Nagy 648 Donát. 1 point: 1 student.

• Problems in Mathematics of KöMaL, April 2010

•  Támogatóink: Morgan Stanley