Track / Stage 6 / 5 of 400 #1005 of 1964

Problem 1005

National Olympiad, first round

Geometry Difficulty 6.0 Prove it KöMaL problem A · Hungary · 2021

For a given quadrilateral $A_1A_2B_1B_2$ point $P$ is called phenomenal, if line segments $A_1A_2$ and $B_1B_2$ subtend the same angle at point $P$ (i.e. triangles $PA_1A_2$ and $PB_1B_2$ which can be also also degenerate have equal inner angles at point $P$ disregarding orientation).

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