Question 7
Question 25. Two towns, $A$ and $B$, lie to the north of a straight road running in the East-West direction (as shown in the diagram below). Unfortunately they are neither connected to the road nor to each other. The people living in the two towns decide to build two new roads, one from each town, to the existing road, such that the route connecting the two towns via the existing road will be the shortest. Given that $AC=10\text{ km}$, $BD=20\text{ km}$ and $CD=40\text{ km}$, find the length of the shortest route from town $A$ to town $B$.
**Editorial input convention:** The two new roads may use a common junction on the existing road. Enter the minimum distance in kilometres.
**Editorial input convention:** The two new roads may use a common junction on the existing road. Enter the minimum distance in kilometres.