Problem

Source: Bundeswettbewerb Mathematik 2023 Round 1 P3

Tags: bundeswettbewerb, geometry



Given two parallelograms $ABCD$ and $AECF$ with common diagonal $AC$, where $E$ and $F$ lie inside parallelogram $ABCD$. Show: The circumcircles of the triangles $AEB$, $BFC$, $CED$ and $DFA$ have one point in common.