Question 8
Answer all ten questions and show detailed solutions. Printed time 60 minutes; each question 4 points. Subcriterion allocations are editorial.
$PQR$ is a triangle. Extend $PQ$ to $S$ so that $PQ=QS$. Point $U$ lies on $PR$ with $PU:UR=3:2$. Lines $QR$ and $SU$ meet at $T$. Find $QT:QR$.
$PQR$ is a triangle. Extend $PQ$ to $S$ so that $PQ=QS$. Point $U$ lies on $PR$ with $PU:UR=3:2$. Lines $QR$ and $SU$ meet at $T$. Find $QT:QR$.