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In triangle $ABC, M$ is the midpoint of $AC$. $O$ is the center of the smaller circle. If $BPTQ$ is a parallelogram, then find $( \frac {BT}{BM})^8$.
Geometry
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In triangle $ABC, M$ is the midpoint of $AC$. $O$ is the center of the smaller circle. If $BPTQ$ is a parallelogram, then find $( \frac {BT}{BM})^8$.