Question 17
Let $ABCD$ be a cyclic quadrilateral such that $AC \lt BD \lt AD$ and $\angle DBA \lt 90^{\circ}$. Point $E$ lies on the line through $D$ parallel to $AB$ such that $E$ and $C$ lie on opposite sides of line $AD$, and $AC = DE$. Point $F$ lies on the line through $A$ parallel to $CD$ such that $F$ and $C$ lie on opposite sides of line $AD$, and $BD = AF$.
Prove that the perpendicular bisectors of segments BC and EF intersect on the circumcircle of ABCD.
Prove that the perpendicular bisectors of segments BC and EF intersect on the circumcircle of ABCD.