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KöMaL 2018 B4970

    A line ee in the plane separates two given points AA and BB of the plane. On the line ee, select points PP and QQ such that ∠PAQ=90∘\angle PAQ=90^{\circ}. Show that there exists a point different from BB that lies on all circles drawn through BB, PP and QQ, independently of the choice of PP and QQ.

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