Physics Cup - 2017, Problem 4

The best solution awards [bonus factor exp(1/4)] goes to all those who either used the approach giving the best possible accuracy - drawing three or four arbitrary lines through O which define two inscribed rectangles of the source circle - or used impressive mathematical rigour in their work:
Gabriel Golfetti
Diogo Netto
Dylan Toh
Richard Luhtaru
Taavet Kalda. [As a non-official participant, he will not reduce the bonus factor down to exp(1/5)]
Finally, there is a late submission with interesting geometrical constructions (like projective geometry, Pascal's theorem) by Navneel Singhal; his geogebra file is also available.

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