VTMO 2026 - Grade 9 - Final - SET 9 - Self-study Question 2

Let square $ABCD$ be inscribed in circle $(O)$. Let $M$ be the midpoint of the minor arc $CD$, and choose $N$ on $AB$ with $NA=2NB$. Line $MN$ meets the circle again at $E$. Reflect $E$ across $AB$ to obtain $F$.

a) Prove $FA=2FB$.

b) Prove $DF=3FB$.