Question

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Explanation:

To prove the two circles are similar, first align their centers with a translation, then adjust the radius with a dilation.

1. Translate $\odot P$ to move its center $P$ to $Q$.
2. The translated circle $\odot P'$ has center $Q$, matching $\odot Q$'s center.
3. Dilate $\odot P'$ by the ratio of the radii of $\odot Q$ to $\odot P$ to match the radii.

Answer:

1. $\boldsymbol{Translate}$ $\odot P$ a distance $PQ$ so that point $P$ maps to point $Q$. So the image of $\odot P$ is $\odot P'$ with center $\boldsymbol{Q}$.
2. $\boldsymbol{Dilate}$ $\odot P'$ using a scale factor of $\boldsymbol{\frac{m}{w}}$. This maps $\odot P'$ to $\odot Q$, so $\odot P \sim \odot Q$.