# 1987 USAMO Problems/Problem 4

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## Problem

M is the midpoint of XY. The points P and Q lie on a line through Y on opposite sides of Y, such that $|XQ| = 2|MP|$ and $\frac{|XY|}2 < |MP| < \frac{3|XY|}2$. For what value of $\frac{|PY|}{|QY|}$ is $|PQ|$ a minimum?