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UKMT Maclaurin Olympiad, 2016

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows two squares $APQR$ and $ASTU$ , which have vertex $A$ in common. The point $M$ is the midpoint of $PU$ . Prove that $AM = \frac{1}{2}RS$ .

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