Shortest Path #2

Geometry Level 3

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

Point PP is on BC\overline{BC} and point QQ is on CD.\overline{CD}.

MM is the midpoint of AD.\overline{AD}.

Let mm be the length of the shortest path from AA to M,M, while visiting PP and QQ sequentially.

Find the value of m2.m^2.

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


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