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$M$ and $N$ start from the same location. $M$ travels $10$ km east ad then $10$ km North-East. $N$ travels $5$ km South and then $4$ km South-East. What is the shortest distance (in km) between $M$ and $N$ at the end of their travel?

1. $18.60$
2. $22.50$
3. $20.61$
4. $25.00$

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