VTMO 2026 - Grade 8 - Semifinal - SET 10 - Self-study Question 8

Trapezoid $ABCD$ has $AB\parallel CD$ and $AB/CD=1/4$. Lines $DA$ and $BC$ meet at $I$. Points $M\in AB$, $N\in CD$ satisfy $AM/AB=CN/CD=1/3$. Line $MN$ meets $AD$ and $BC$ at $P,Q$, respectively. Given $IP=IQ$, find $AD/BC$.