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A. 614. In the triangle $\displaystyle A_1A_2A_3$, denote by $\displaystyle k_i$ the excircle opposite to $\displaystyle A_i$, and let $\displaystyle P_i$ be the point of $\displaystyle k_i$ for which the circle $\displaystyle A_{i+1}A_{i+2}P_i$ is tangent to $\displaystyle k_i$. ($\displaystyle i=1,2,3$; the indices are considered modulo $\displaystyle 3$.) Show that the line segments $\displaystyle A_1P_1$, $\displaystyle A_2P_2$ and $\displaystyle A_3P_3$ are concurrent.

(5 points)

Deadline expired on 12 May 2014.

Statistics on problem A. 614.
 1 student sent a solution. 3 points: 1 student.

• Problems in Mathematics of KöMaL, April 2014

•  Támogatóink: Morgan Stanley