VTMO 2026 - Grade 8 - Semifinal - SET 09 - Self-study Question 8

Square $ABCD$ has side $3$. Points $M,N,P,Q$ lie on $AB,BC,CD,DA$ with $AM=BN=CP=DQ=1$. Diagonal $BD$ meets $MN$ at $E$ and $PQ$ at $F$. Find $EF$.