USAMO

Geometry Difficulty 6.0 National Olympiad Find the answer

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?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

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