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A. 672. Point $\displaystyle O$ is the apex of an oblique circular cone. Show that there are some points $\displaystyle F_1$ and $\displaystyle F_2$ in the interior of the base such that $\displaystyle \angle XOF_1 +\angle XOF_2$ is constant when $\displaystyle X$ runs along the perimeter of the base disk.

(5 points)

Deadline expired on 10 June 2016.

Statistics on problem A. 672.
 5 students sent a solution. 5 points: Cseh Kristóf, Schweitzer Ádám, Williams Kada. 4 points: Bukva Balázs. 1 point: 1 student.

• Problems in Mathematics of KöMaL, May 2016

•  Támogatóink: Morgan Stanley