Problem

Source: USAJMO 2020/4

Tags: USAJMO, geometry, 2020 USAJMO, geometry solved, Angle Chasing, easy, usojmo



Let $ABCD$ be a convex quadrilateral inscribed in a circle and satisfying $DA < AB = BC < CD$. Points $E$ and $F$ are chosen on sides $CD$ and $AB$ such that $BE \perp AC$ and $EF \parallel BC$. Prove that $FB = FD$. Milan Haiman