2005 IMO Problems/Problem 5


Let $ABCD$ be a fixed convex quadrilateral with $BC = DA$ and $BC \nparallel DA$. 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 $R$. Prove that the circumcircles of the triangles $PQR$, as $E$ and $F$ vary, have a common point other than $P$.


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See Also

2005 IMO (Problems) • Resources
Preceded by
Problem 4
1 2 3 4 5 6 Followed by
Problem 6
All IMO Problems and Solutions