VTMO 2022 — Grade 8 — vtmo Question 10

Square $ABCD$ has side $3 \,\mathrm{cm} , M , N , P , Q$ on $AB , BC , CD , DA , AM = BN = CP = DQ = 1$. $E , F$ are $BD$’s intersections with $MN , PQ$. Find $EF$.