# Shortest Path #2

Geometry Level 3

There is a rectangle $$ABCD$$ with side lengths 2 and 3 as shown on the right.

Point $$P$$ is on $$\overline{BC}$$ and point $$Q$$ is on $$\overline{CD}.$$

$$M$$ is the midpoint of $$\overline{AD}.$$

Let $$m$$ be the length of the shortest path from $$A$$ to $$M,$$ while visiting $$P$$ and $$Q$$ sequentially.

Find the value of $$m^2.$$

This problem is a part of <Shortest Path> series.

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