Mathematical and Physical Journal
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Problem A. 474. (February 2009)

A. 474. The point Q is located in the convex n-gon P_1P_2\ldots P_n. Show that

\sum_{k=1}^n \big(\cot QP_{k-1}P_k\sphericalangle +
\cot QP_{k+1}P_k\sphericalangle\big) \cdot \overrightarrow{QP_k} = 0.

(The indices are considered modulo n, e.g. P0=Pn and Pn+1=P1.)

(5 pont)

Deadline expired on March 16, 2009.


7 students sent a solution.
5 points:Éles András, Nagy 235 János, Nagy 314 Dániel, Nagy 648 Donát, Tomon István, Tossenberger Anna, Varga 171 László.

Problems in Mathematics of KöMaL, February 2009