Question 4
Let $ABCD$ be a convex cyclic quadrilateral with $DA\lt AB=BC\lt CD$. Choose $E$ on $CD$ and $F$ on $AB$ such that $BE\perp AC$ and $EF\parallel BC$. Prove $FB=FD$.
Proposed by Milan Haiman. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p15952890. Source video https://youtu.be/r7j0oRtpErA?t=3960.
Proposed by Milan Haiman. Evan Chen’s third-party compilation; source discussion https://aops.com/community/p15952890. Source video https://youtu.be/r7j0oRtpErA?t=3960.