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Solution
This time, the best solution award was distributed evenly among those simplest geometric solutions which were submitted before the hints. Let us proceed in the chronological order.
The solution of Ion Toloaca:
Case 1:
Next, the solution of Nikita Sopenko:
Next, the solution of Jakub Šafin:
 
Finally, the solution of José Luciano de Morais Neto:
Non-geometrical solutions are significantly more complicated. Attila Szabó's solution is also mostly geometrical, and not that complicate d:
His Geogebra file can be retrieved here.
Stefán Alexis Sigurðsson's solution shows how complex things can become:
Another quite long arithmetic solution is provided by Jun-Ting Hsieh:
And one more arithmetic/trigonometric solution, provided by Kohei Kawabata:
The last example of arithmetic solutions is that of Nadezhda Vartanian:
  
And the very last example is the contribution of Ivan Tadeu Ferreira Antunes Filho – although sent a little bit late, but still a nice and short one:
And so, that's it for this year. Thanks to all the participants for a large number of wonderful solutions! If Physics Cup will continue next year is not yet clear…
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Jaan Kalda
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