\(\qquad\)Let \(ABCD\) be a fixed convex quadrilateral with \(BC = DA\) and \(BC\) not parallel with \(DA\). Let two variable points \(E\) and \(F\) lie of the sides \(BC\) and \(DA\), respectively and satisfy \(BE = DF\). The lines \(AC\) and \(BD\) meet at \(P\), the lines \(BD\) and \(EF\) meet at \(Q\), the lines \(EF\) and \(AC\) meet at \(R\). \(\\\qquad\)Prove that the circumcircles of the triangles \(PQR\), as \(E\) and \(F\) vary, have a common point other than \(P\).
| Attributes | Олімпіадна |
|---|---|
| Source | International Mathematical Olympiad |
| Year | 2005 |
| Number | 5 |
| Difficulty | 10.0 |
| Themes | Геометрія |